I've looked over the class and I couldn't find the answer. I notice that they do have UMD and I suppose that's there for a reason. If there is a difference between the use of spell completion and spell trigger and the spells that they actually chose to be able to cast, it'd be great if you could let me know. Thanks!
gather information :
If the item (wand, scroll, etc) contains a spell that a Summoner can cast (e.g. it is a spell on the Summoner's spell list) then they can use the item without needing to roll any UMD check. Otherwise it is the same as any other class using an item with a spell they can't cast (cleric with a wand of magic missile, rogue with a wand of CLW).
Spell Completion: This is the activation method for scrolls. A scroll is a spell that is mostly finished. The preparation is done for the caster, so no preparation time is needed beforehand as with normal spellcasting. All that's left to do is perform the finishing parts of the spellcasting (the final gestures, words, and so on). To use a spell completion item safely, a character must be of high enough level in the right class to cast the spell already. If he can't already cast the spell, there's a chance he'll make a mistake. Activating a spell completion item is a standard action (or the spell's casting time, whichever is longer) and provokes attacks of opportunity exactly as casting a spell does.
Spell Trigger: Spell trigger activation is similar to spell completion, but it's even simpler. No gestures or spell finishing is needed, just a special knowledge of spellcasting that an appropriate character would know, and a single word that must be spoken. Spell trigger items can be used by anyone whose class can cast the corresponding spell. This is the case even for a character who can't actually cast spells, such as a 3rd-level paladin. The user must still determine what spell is stored in the item before she can activate it. Activating a spell trigger item is a standard action and does not provoke attacks of opportunity.
I could be wrong, but when I read this it sounds like:
Spell trigger: If you are of a class that can cast the spell then you can cast that spell without needing to use UMD.Spell completion: You must have the spell on your spell known list to use it without UMD.
But I had always thought both were usuable as long as you had the spell on your class list. Though, it makes more sense as I originally stated because sorcerers have UMD as a class skill which they would need to use to activate spell completion items for spells they can't actually cast on their own.
Spell Trigger (e.g. Wand) can be used by anyone that has the spell available to their class, even if they don't know that spell, even if they are not high enough level to cast it themselves - all they need is to belong to a class that has the spell on the class list.
Spell Completion (e.g. Scroll) can only be used by someone who is capable of casting the spell. He must have it on his class list AND must be of a high enough level to cast that spell. If he has it on his class list but his level is too low to cast it, he can still try but might fail.