It doesn't. I believe that is stated in the Ultimania guides as fact (though technically, they're summoned by Yu Yevon, not the fayth which merely provide the raw information that YY can use when summoning). As for Tidus, my only guess is that to possess Tidus, he'd have to possess all of DZ (like he had to possess all three Magus Sisters) and that may just not be possible for Yu Yevon.

The only issue this possibility raises is why was Yu Yevon able to possess Jecht. I think the way around this is to consider that YY possessed Braska's Final Aeon, and not Jecht. Treat the two as different entities. He couldn't possess Jecht as a human Aeon, but when he became a Fayth and Final Aeon too, that he could capitalise upon...