It was probably intended to just let you play as more characters unless Cortez has some sort of technology that gives him a disguise for each time period. --- Montages, Commentaries and Gameplays: http://www.youtube.com/user/ZAV1010
This is just my opinion, but I think it could be because the previous time travel device didn't allow Cortez to have his psychical body, instead having to borrow somebody else's as long as he was in that particular time.
Then he brought back the Time Crystals to Earth and they were used to power a more efficient time machine, and he was able to keep his body as he traveled through time. Again, this is just an opinion :P