People move across considerable distances and settle someplace. If there isn't anybody there to begin with, or if the newcomers exterminate the older population, the issue is simple, for no gene mixture occurred, the new new genes are there, in a new place, that's it. But if there is a population already there and admixture occurs, the newcomers' genes have joined in what is now a new genetic pool. The second form of genic exchange is gene flow. This differs from migration in that nobody moves around very much.
People are like the individual drops of water bobbing up and down in the ocean.
But they mate with the people in the next tribe, perhaps as a matter of established custom, and the people next door also mate with people over on the other side, and so on, and given enough time a highly useful genetic trait can spread pretty far. That sets the general scenario. I think it very likely that in the earliest days of our sapient ancestors' existence their genes spread far and comparatively rapidly, both through migration and through gene flow. In due course, everyone around who qualified as homo was sapiens, there were no longer any erecti left. The precise history of what happened to whom and when, who went where, during that early period of expansion, will probably never be known.