Dinosaur King/WMG

The Alpha Gang or some other force caused the dinosaurs to gain superpowers by putting them into cards
Dr. Z has been shown at some points to be able to modify cards. Either he, or some other force from his time, must have traveled back in time (the Alpha Gang is shown to have a Time Machine after all) to capture dinosaurs in order to turn them into Mons for entertainment in the future.

Rex Owen is an alternate universe Emil Castagnier

 * Well, look at how similar they are in design. Maybe he was reincarnated into another universe after his human self's death by old age or what have you.