OK, let me try and timeline this so I can understand it better.

1000 years ago: Bevelle and Zanarkand are at War. Zanarkand is losing, badly. The city is blitzed by Bevelle and only a few survivors and their leader, Yu Yevon are left. The citizens of Zanarkand, in order to continue on in some form, agree to become Fayth to summon Dream Zanarkand, a location which is exactly as Zanarkand was before, away from the world. They do so, and Yu Yevon devotes himself to this task. However, to protect himself he creates Sin, an armour that, intentionally or not, has an intrinsic desire to destroy. Yunalesca, the daughter of Yu Yevon and her husband Zaon attempt to stop Sin by creating the "Final Aeon", using her husband as a Fayth so powerful that it causes Yunalesca to die during the summoning process. However, this doesn't work according to plan. While the Fina Aeon defeats Sin by piercing it's armour, Yu Yevon simply possesses this Aeon. I'd assume that Yu Yevon died in this initial onslaught. Using this host body he could continue to summon Zanarkand and maintain Sin. As such the Yevon temple is created to "appease" Yu Yevon, believing that the use of Machina in the war is what caused Sin to appear, using this as a scapegoat. As such the tradition of pilgramidges starts, since no one can figure out how to defeat Sin any other way. If the strongest Aeon ever can't pull it off, what can?

Ten years before FFX: Dream Zanarkand has been around for nearly a thousand years, unaware of Spira and it's true nature. Jecht, whilst out far into sea Bliztball training comes into contact with Sin who happens to be in the neighbourhood. He is "snagged" by it and brought to the mainland, where he meets Braska and Auron and agrees to go on Braska's pilgramidge, initially hoping that finding Sin may enable him to go back home. However, over time his resolve changes, eventually realising that he cannot go back home (presumably the Fayth that create Dream Zanarkand spoke to him like they did Tidus). He becomes the Fayth for Braska, and thusly pierces Sin, becomes possessed and eventually becomes Sin once more.

During FFX: Tidus is taken from Dream Zanarkand after Jecht returns there, having some minor control over Sin. Since Sin is destructive it attacks Dream Zanarkand. Whether or not it is destroyed is up to interpretation. Presumably a new Dream Zanarkand could be created. Events happen in FFX, up until the party learn the truth. So they devise another way to defeat Sin: Destroy the Final Aeon within, allow Yu Yevon to possess the remaining Aeons and destroy them, leaving Yu Yevon without anything to possess, thusly destroying it. No Yu Yevon, no Sin, no Dream Zanarkand or it's peoples. Thusly Tidus loses his link to Spira and is sent to the Farplane like all other souls are.

Is that about right?