Nononono, Summoners and Fayth existed in the wayway back before Yevon made a last ditch effort to save the peoples of Zanarkand by making them Fayths. This is how I understood it:

So the Summoners of Zanarkand and the people of Bevelle have this great big war, and the Summoners are ttly losing. Yevon, who was probably some super awesome big Summoner priest guy came up with a last ditch effort to protect Zanarkand and seek revenge on the rest of the world. He convices/forces the people of Zanarkand to sacrifice themselves and become a huge part of one giant Fayth/Aeon. The dream Zanarkand is so called because it exists only as a dream of the sleeping Fayth. Yevon then uses the power of this Fayth to create Sin, his roving monster that no one can stop and he controls. But, as usual, absolute power corrutps absolutely and he goes crazy and kills anything in his path. But there's a problem. We find out that Sin actually does have weaknesses, it can be beaten it can die. So Yunalesca comes up with this plan to feed it more Aeons, allowing it to merge with them and keep on punishing the world for it's dastardly ways. She invents the religion, she goes on the first pilgrimmage and whacks her boyfriend to feed to Yu-Yevon/Sin so they can keep on punishing them some infidels who dare use technology forver and ever.

Meanwhile, Dream Zanarkand still exists to perpetuate what the Summoners wanted to have and power Sin around the world so it can kill stuff in between feedings. Remember there's no machina in DZ. And also no of whatever they called Rikku's people. Can't remember. The Zanarkanadians... They a bunch of racists.

Unfortunately they call one of their big gun Fayth's out (Jecht) to feed to Sin. He still has a heart, he tells Auron stories about his son and they all figure out what's going on. Auron is pissed as hell, tries to kill Yunalesca so she can't make anymore people go on this stupid journey but he dies in the process. However, he's such a badass that he makes himself his own Fayth, his own Aeon, and crosses over to Dream Zanarkand to find the only entity he figures can reach out to JechtSin - his son Tidus.

But maybe I'm Future Esthar crazytalk here lol