Nah, the hardcore extermination was happening waaayyyy before Euros crossed the Mississippi. During the Beaver Wars in New York and around Ohio, native civilians were brutally murdered, scalped, impaled, and generally just constantly harrassed until entire cultures were pushed into the swamps around the Great Lakes (that were havens for malaria-carrying mosquitos). Then during/after the Northwest Indian War, the Americans pushed them out of the swamps and out to Oklahoma along with the Cherokee. And they did the same thing again with Tecumseh's multicultural project, the Miami, and the Potawotami in Indiana/Michigan. If the pretext of "treaties" were not followed then the inhabitants of the area were forcibly removed by the military as "aggressors". The regions east of the Mississippi have some of the lowest native populations to this day, despite having thriving agricultural civilizations at the time of the De Soto expedition (it's generally understood that De Soto's crew were probably the only Euros to witness/record Mississippian culture firsthand before it was wiped out by smallpox).