But see, that brings back the whole, how can Machiavelli control time? issue. Only the codex and Chronos have the secret to time itself.
Him sending them to another strand that is on the same time plane makes more sense, as he didn't manipulate time itself he just manipulated the strand Joan and Scatty were on.
On "our" strand the dinosaurs died out millions of years ago. On the strand Scatty and Joan are on, it's still 2007, just that the dinosaurs are still running strong (or at least a few of them are)