This is a tough question and I don't think I've ever come across a good definition or any criteria. Part of the problem is that the realization that people moved around a lot before Europeans showed up, is kind of a recent phenomenon. It's obvious if you think about it for a few minutes, and it's even evident in texts, but it wasn't really considered important until the late 60s when cultural studies got established and people started seriously researching the question.

It's interesting how unseriously your question was taken until the last few decades b/c we have stories and information like part of the "Aztec" origin myth is that they migrated to the Mexico City valley in waves between 600 and 1000 CE, so it was staring us in the face the whole time. Another interesting one is when the Spaniards first arrived in Texas they were approached by Jumano people who were looking for allies b/c they were being pushed out of the area by Comanche and Apache peoples.