
Sphynx |

The objective here is just to make the archetype as interesting mechanically, as it is thematically. It's, for the most part, a rewrite though. Note: Electrical Polarity has been removed meaning that the storm caller gains access to the shield ally and greater shield ally of the summoner.
Summon Storm's Fury - Lightning Bolt (Sp)
A storm caller can, at 1st level, cast lightning bolt as a spell-like ability, as a standard action with a caster level equal to his summoner level. This replaces the 1st level of the summon monster class feature. Using this ability does not count against the number of times the storm caller can use the summon monster class feature.
Summon Monster I (Sp)
When summoning monsters using the class ability, the storm caller is limited to one of the following:
I - Replaced by Summon Storm's Fury - Lightning Bolt
II — small air elemental, small lightning elemental;
III - Replaced by Summon Storm's Fury - Call Lightning
IV — medium air elemental, medium lightning elemental,
V — large air elemental, large lightning elemental;
VI — huge air elemental, huge lightning elemental;
VII — Replaced by Summon Storm's Fury - Call Lightning Storm
VIII — elder air elemental, elder lightning elemental
IX — advanced elder air elemental, advanced elder lightning elemental.
All summons via this ability gain immunity to electricity. If a group of elementals is summoned, due to summoning a lower level of creature for the spell level, each elemental can cast lightning bolt as a spell-like ability, with an effective level equal to the spell level of the spell (so elements summoned with a spell equivalent of summon monster IV would be treated as being 2nd level for purpose of the lightning bolt), with a minimum effective level of 1. Each summon that gains this feature, may only use it once.
Summon Storm's Fury - Call Lightning (Sp)
At 5th level, as long as his eidolon is within 100', the storm caller can expend one use of his summon monster class ability to cast call lightning as a spell-like ability with a caster level equal to his summoner level, except as noted below. This can even be done while he has summons active from his summon monster class ability.
Each bolt of lightning deals 3d6 points of electricity damage. This damage increases by 1d6 at 7th level and every 2 levels thereafter, to a maximum of 10d6 at 19th level. The prevailing weather has no effect on the damage of the lightning bolts. The Reflex save DC is equal to 10 + half the storm caller’s summoner level + his Charisma modifier. If the storm caller uses this ability again before he has used all of his available bolts of lightning, any unused bolts are expended with no effect.
This replaces the 3rd level of summon monster
Aspect of the Storm (Su)
At 10th level, a storm caller gains a flight speed equal to his eidolon, with the same maneuverability of his eidolon. This has no cost in the way of evolution points. This replaces the aspect and greater aspect of the summoner.
Summon Storm's Fury - Call Lightning Storm(Sp)
At level 15, the storm caller may replace call lightning with call lightning storm when using the summon storm's fury - call lightning
This replaces the 7th level of summon monster
I feel this lines up better with a vanilla summoner, both thematically (Ie: replacing Aspect instead of positioning, for an aspect), and mechanically. Thoughts before I go adding it to my list?

Sphynx |

Summon Storm's Fury - Lightning Bolt (Sp)
A storm caller can, at 1st level, cast lightning bolt as a spell-like ability, as a standard action with a caster level equal to his summoner level. This replaces the 1st level of the summon monster class feature. Using this ability does not count against the number of times the storm caller can use the summon monster class feature.
This is/was too powerful, especially at the low-mid levels. As our level 8 Aerokineticist pointed out, 8d6 is still more than his own 4d6+6. So, we agreed it was fair to use level/2 instead of level.
Rewrite:
Summon Storm's Fury - Lightning Bolt (Sp)
A storm caller can, at 1st level, cast lightning bolt as a spell-like ability, as a standard action. Caster level for this class feature is equal to half of his summoner level, with a minimum of 1d6. This replaces the 1st level of the summon monster class feature. Using this ability does not count against the number of times the storm caller can use the summon monster class feature.
All summons via this ability gain immunity to electricity. If a group of elementals is summoned, due to summoning a lower level of creature for the spell level, each elemental can cast lightning bolt as a spell-like ability, with an effective level equal to the spell level of the spell (so elements summoned with a spell equivalent of summon monster IV would be treated as being 2nd level for purpose of the lightning bolt), with a minimum effective level of 1. Each summon that gains this feature, may only use it once.
The intent was that the level of the elemental was treated as the level of the Summon Monster spell -2, so Summon Monster IV would be treated as a level 2 caster.
So, at 11th level, other Summoners could summon d3 Bralani Azata for 7d6 to 21d6. Since that's a level 6 Summon Monster, in our version that should be 4d6 (treated as level 4) to 20d6 if you summon 1d4+1 medium air/lightning elementals. Weaker hits, slightly weaker total damage, only once instead of twice, but scales to level.
So, to get a view of it...
Summon Monster IV: 1d4+1 small elementals doing 2d6 lightning bolts, once each (First level that they can use lightning bolts, max 10d6 total).
Summon Monster V: 1d3 medium elementals doing 3d6 lightning bolts, once each (max 9d6 total, likely better to use the IV version, but this is better for penetration).
Summon Monster VI: 1d4+1 medium elementals doing 4d6 lightning bolts, once each (Max of 20d6 total).
etc...
Rewrite:
All summons via this ability gain immunity to electricity. If a group of elementals is summoned, from summoning 1d3 or 1d4+1 creatures for the spell level, each elemental can cast lightning bolt as a spell-like ability, with an effective level equal to the spell level of the spell -2 (so elements summoned with a spell equivalent of summon monster IV would be treated as being 2nd level, for purpose of the lightning bolt). Each summon that gains this feature, may only use it once.
I'm not 100% sold on it, after all, that's still a LOT of damage... admittedly, not anymore than a vanilla summoner, but feels like it is a lot.

Azothath |
thinking about it...
my first read says is it is overly focused on lightning bolts(evocation) and call lightning(evocation), aka doing all one type(aka [electric]) of damage and it is a conjurer.
It is a school issue, a thematic issue, and a focus on 'just one type of damage' issue which does not make the class weaker but opens it to nullification via Resist Elements [elec] and Protection from Elements [elc]. Those are cast by wizards and druids mostly.
For a summoner focus on summoning - air, lightning, water, tumblespark, mephits, mist dragon, hungry fog, cloud dragon, mist creatures(template), Gyeongsa, wind effects, sonic effects, etc. I that will bring it back to some semblance of balance as you are curating the summon's lists rather than creating a themed evoker.
If you want to do an evoker, copy wizard Evoker, ditch the eidolon or make it a storm elemental.
To put it another way, you want the summonings of a summoner and the blasty part of an evoker. Two of the better casters in one. I'm pretty sure you are directly headed for balance issues from the get go.

Sphynx |

This isn't me trying to invent an archetype, it exists: https://www.d20pfsrd.com/classes/base-classes/summoner/archetypes/paizo-sum moner-archetypes/storm-caller-summoner-archetype/
The goal is just to make it playable (Hence the (Unchained)). My player wants to play this because of theme (nothing to do with being an 'evoker'), and I don't want him to feel side-lined because he can't keep up with the players. He's already going to suffer heavily because many high level mobs are immune to electricity, but at least he'll have fun (hopefully) getting to that point.

Azothath |
here's the link to the official one Summoner arch Storm Caller
note the special eidolon required (or nauseated)
ist half of Summon Storm - curated summons list
2nd half of Summon Storm (call lightning) is pretty ineffective except on mooks (CR=APL-2 martial types).
The Elec Polarity just repeats the 2nd half above. As it all costs a special summons, it is worse than the summons over the long haul.
Storm's wings is good as flight is good.
The special summon monster list really needs expansion as the base Unch Summoner uses the regular list. See my first post.
Normally dice are (cstrLvl, max 10)d6[elec] so they are running at half damage.
The call lightning damage is lower as it's a long term spell, so that's okay.
The Elec Polarity if using the same dice needs to have a save for staggered or stunned to give it more punch.
Lightning bolt has different criteria, the effect is closer to SLA lightning arc:K5 with the two endpoints not taking damage as if a metamag was applied (so +1 SplLvl). I'd be very hesitant to add a 4th-5th level SLA to any class. Rather than adding an SLA, I'd look at the added condition or upping the dice to the standard.
Their imm/rst[elec] leaves open the grapple-zap attack using the eidolon and caster's action.