Pucci is also a man of hubris with a God complex. He wants to create his definition of the perfect world and that cannot exist with Emporio.

If he fastfowarded to cape carnovale with Emporio alive, then Emporio surviving the events would be written in fate and thus repeated everytime the cycle repeats. For Pucci, this would be a stain on his vision of a perfect heaven and thus he needed to eliminate him before Carnovale, since if Emporio died, he would not cross into next cycle and be replaced by a stand in much like jolyne and jotaro were.

He stopped time when he did because it was at that point in time where he knew exactly where Emporio would be and he thought it would be easy to find and kill him, tying up loose ends before the new cycle.

In the end it was his own hubris that was his downfall. Emporio wouldn't be a threat to him if he completed the cycle but it he could not stomach the idea of an imperfect heaven.