Summoner's lore theory starting in EW based on job actions (Pre-expac)

Carbuncle is the base summon/familiar who strengthens and works with the summoner.

Summoners can draw on ambient destructive aether following the Calamity to summon and maintain a Bahamut construct.

While the construct exists, the summon can use it's aether to augment their own power (Astral Flares/Impulse).

When Bahamut dissipates the summoner can draw on the aether absorbed from Ifrit, Titan and Garuda (the Triad). This aether is limited to a small amount so only a quick, small manifestation can be made, using their ultimate ability before dissipating. Upon dissipating the ruby, emerald and/or topaz gems are infused with the pseudo-primal's elemental aspected aether. The summoner uses Carbuncle as the conduit to use the elemental aether allowing Gem abilities to be used. Once the elemental aether has been used, the next pseudo-primal can be called.

After some time the summoner can draw on ambient aether left behind during the the rebirth of Eorzea to summon a Phoenix construct, which empowers the summoner just as Bahamut did.

(Side note: It's possible the 3 "gems" are, in fact, the singular gem used to form Carbuncle. As a jewel, like a ruby, is used to manifest the familiar that same jewel may be able to absorb the elemental aether from the Triad)

Hopefully this makes sense to people other than myself haha In any case, enjoy!!