First and foremost is their appearance. These people--let's call them Atlanteans--have bald heads, topknots of hair, and pendants in their ear lobes. This was a very typical look among the Maya.
A good example of this look is the non-Maya Black Hawk, war chief of the Sauk Indians (below). He would've fit right in with the Atlanteans of 10,000 B.C.
What it means
This is just speculation, but at least two theories explain the movie's "facts":
1) The Atlanteans seeded both the "New" and "Old" Worlds with their culture and technology. Hence both sides had the same type of monumental architecture.
2) The Atlantean culture arose in the Western Hemisphere--one of those lost Mesoamerican civilizations so often seen in fiction. It eventually disappeared, but its impact was lasting enough to influence later Mesoamerican cultures.
For more on the subject, see The Best Indian Movies.