There are plenty of folks who came over after the bulk of the genocide was largely done. Don't think an Italian coming over in the 1910s had fuck all to do with the Native American genocide.

But even ignoring that you are assuming that this is all a black and white situation when people are rarely that. For example the early Scots-Irish population in Appalachia generally got along well enough with native Americans often times even mixing together, you could also have the later Irish immigrants from the Irish genocide by the English inflicting the same fate apon Native Americans in the great planes.

Hell my own ancestors did seemingly contradictory shit as being slavers while murdering people for being bigots against Native Americans. Only for a generation later to be fighting for the abolishment of slavery and arming natives while really fucking hating newer Anglo settlers to the point of commiting hate crimes.