But this isn't a metamagic rod: If you look at the construction requirements it would seem RAI that it would work with the summoner's SLA - it would be pretty silly to have an item where the SLA allowed you to meet the construction requirements but then couldn't use the same SLA with it!
In addition there is this (my bold):
Owen K. C. Stephens wrote:
There is a distinction here, and it's subtle, but important. When you add a metamagic feat to a spell-like ability, you end up having to use a spell-like slot one or more levels higher. Since there is no such thing as a spell-like slot, you can't use your metamagic enhanced spell-like ability. (If you add metamagic feats with a +0 level modifier from some other source, they'd work fine with spell-like abilities).
Augment Summoning, however, along with Spell Focus, Spell Penetration and the greater versions of same, has no need for a spell-like slot to function. Thus they work just fine with spell-like abilities in addition to spells.
I'd say it was pretty clearly meant to work with the summoner's SLA.