Summoner:
Primals must be fought to be a summoner; the idea is that when a primal dies, anyone nearby is soaked in the resultant aether. Once any prospective summoner has gained a touch of the primal's aether, they're able to summon an egi of that primal from that aether,. Once defeated, that primal is dominated by the Summoner; this allows them to summon them at will. However, the current maximum of egis is 3. To compensate, Summoners are able to enter a Trance state based upon the power of a primal. The example we see in-game is Bahamut, who touched everyone with his aether due to the Calamity. In theory, this can be done with any primal, but Bahamut was the most powerful at the time, and thus is the one that was picked. (Warring Triad Trances in the future? )

We know all of their spells originate from Allag and have been gleaned from Tomestones, so it's most likely still along the lines of ACN: arcane geometry guiding their abilities.