But think about Auron's past as well. For one thing, he's more mature than Tidus. Auron has also been on an adventure before, so in a way, he's used to being away from home.
Tidus is a blitzball star living in Zanarkand and had father issues. During one of his games, Sin attacks Zanarkand and Tidus is then sent 1000 years into the future, along with Auron, though they are separated.
The difference is that Tidus is in shock. Auron probably expected this (I may be wrong on that). Tidus has no idea where he is, and there's no one there with him. He's lonely, which is something he's rarely has to feel because he gets so much attention for Blitzball. After finding out that he's 1000 years into the future, do you know how shocking that could be? That you would never be able to see your beautiful hometown again? And wouldn't that make you worried as to why you were sent into the future in the first place? Tidus' reaction is totally understandable.
Auron has had too many experiences to complain. And I think he expected this anyways because he seemed to know exactly what was happening when Sin was attacking Zanarkand.
