Where does it state that the people of Zanarkand willingly became Fayth?
The Bevelle Fayth specifically says they all wanted to save Zanarkand which means they all willingly gave themselves to become Fayth.

"Yes. A war between Zanarkand and Bevelle. Bevelle's machina assured their victory from the start. Spira had never seen such power. The summoners of Zanarkand didn't stand a chance. Zanarkand was doomed to oblivion. That's why we tried to save it -- if only in a memory."

There is no mention of it being all Yu Yevon's doing.

If maintaining Dream Zanarkand was the only reason for Sin's existence, then what about Sin's other thing, wiping out any large cities? "Yu Yevon gave this creature a set of very simple instructions: destroy any machina or settlement which grew larger than a small village in order to bring technical evolution to a halt, and retaliate to all hostility with extreme prejudice." - you be the judge of what Yu Yevon's intentions for these instructions were.
As far as I can remember reading in a translation of the FF Ultimania, it was to prevent people from discovering the island where Dream Zanarkand was being summoned. DZ is in fact a "real" place which would explain how Sin travels from it to regular Spira no problem. Sin alone can travel pretty much every corner of the globe because limited technology keeps people from freely exploring.

At least this is what I remember reading and it's really stupid which is why i tend to ignore it.