I've always wondered about the exact relationship between these two. I figured he was a guardian to Tidus (by which I mean someone who stands in for the parents of a minor) rather than the classic creepy karate master who observes from a distance and pulls a deus ex machina if something goes wrong.
Flashbacks suggest to me that he was at the very least a family friend, even a member of the household, but how the hell would you do that? If you met a weird man, supposedly washed up on the shore and unable to wear his coat correctly (what's up with that anyway), would you let him near your seven year old son? Maybe if he had 'proof' that he knew Jecht, like a written statement with his autograph on it, but that would get him a whole lot of unneeded attention for having met a really famous missing person.
I also get chuckles from imagining Auron in a parental role, cooking dinner for Tidus and the like. I'm reckoning Dream Zanarkand has no education system, but I'd love to see Auron helping Tidus with his homework. Tidus was orphaned for the greater part of his life, so Auron must've done a lot in the way of raising. Can anyone give me their opinion on how Tidus acts regarding his age? I'm bad at these things.