The Aeons that have existed for hundreds of years are, indeed, summoners from the remnants of Zanarkand —

I think that it was established in the game that the Final Aeon is a special exception to the rule, yet, at the same time, is no different from an ordinary Fayth because Anima can be summoned by Yuna, Seymour, and the Guado summoners without any special connection to the Fayth itself.