Actually, no, it's not.
DZ time moves at the exact same speed as Spira (give or take a few microseconds). This means that just as Spira has survived for 1000 years after Sin, so too has DZ grown and evolved. At the time of its creation, DZ might have been nearly identical to the real Zanarkand, but just as Yunalesca says, how do you expect to keep an eye on everyone all at the same time? Just as it is in witness statements, things can vary quite differently. Over the course of time after it was established, the people in DZ grew and evolved; they loved, died, did what they do. After a certain point, Tidus was created, probably based on a recycled Shuyin template.
Is Tidus the same as Shuyin? No, he isn't. The two are quite different, despite their tendencies to be incredibly selfish when it comes to their women.
Yu Yevon can sometimes reset the city, incase something goes bad, but this changes very little.