She's half correct about the reincarnation. The passage of time in DZ is that of Spira's (because as we should know, DZ has a physical location in Spira). It is very likely that in the original dream, Shuyin was recreated by the Fayth. However, he would've eventually gone and died, since the Fayth at the time probably did not know of his demise, and they certainly would not have known that he was slowly going nuts inside the Den. Dream Shuyin does not suffer this fate; he could have done anything else. Since the War did not occur in DZ, it's not unreasonable he lived out the rest of his life with Lenne. Say Dream Shuyin had kids. It's not unfeasible that Tidus' template was based on Shuyin's, if he were a descendant.

Alternatively, Yu Yevon could've reset DZ (as he is said to be able to do) and simply based Tidus off of Shuyin's template. After 1000 years, you're bound to run out of ideas somewhere.

As for Tidus, it's pretty simple. The Fayth dreamt up DZ, and Tidus was a part of it. At the end of FFX-2, they simply decided to keep dreaming one part of the dream, since, you know, Yuna more or less gave them their freedom.