Hello John and Connie,
The Ethnicity results you receive from the testing companies are based on who has already tested within their DNA Pool of individuals and how you stack up with those results. As more people test your results may shift and change because the information they draw from is constantly changing.
Also when they are talking about ethnic results they are looking a deep Ancestry. We all came out of Africa then over 100k years or 200k or 30k years our haplogroups mutated and became something different from what they were originally.
So first rule of thumb is that ethnicity results are shifting sands.
If the indigenous population followed a land bridge or crossed the oceans or skipped along the ice sheets to the American Continent in early times they would have arrived as indigenous peoples from where ever they came from. So some populations in northern Europe, Asia, Russia, Indonesia... (you get the idea) would have some DNA spread to the American continent as well as leaving some DNA behind in the individuals who did not migrate.
This is a very general explanation - check out this 2013 post from Roberta Estes for more - you can also google your question too.