Hmm. Auron got to Zanarkand after Braska defeated Sin, so that would've been about the time that Jecht first became Sin. Auron, near death thanks to Yunalesca, first made sure that Yuna was going to be cared for, then he set off to honour his promise to Jecht by finding a way to Zanarkand to watch over Tidus. Sin can go into the 'dream world', we know that much. Auron 'rode' Sin to get to Zanarkand; Jecht undoubtedly had a hand in that. Sin's a huge living creature, full of very real monsters and the body of Yu Yevon; yet all of these corporeal beings can make the transition into the 'dream world', probably by getting reduced into that same ethereal energy seen at Mount Gagazet. A reversal of the procedure that allowed Tidus and Jecht to become real, in other words. It can work one way, why not the other?
That's also a possible explanation for Auron ageing, while the other unsents remained the same - once in the 'dream world', he became a fully living, normal person once again. Then, when the time came, both Auron and Tidus left the 'dream world' by way of Sin. "You are sure?", Auron asks, just to be certain that Jecht's not going to change his mind or regret throwing his son into that mess.