A good portion of the deaths came from diseases they had no immunities too. They would have eventually ran into European, African, and Asian viruses. Europe lost like half it's population during the black plague and has been hit with plagues for millennia. It's nothing new the devastation that can happen. It wasn't just smallpox the natives got hit with. It was a whole array of diseases.
Smallpox, Measles, Influenza, Whooping cough, Typhus, Mumps, Chickenpox..diseases that Europeans had immunities too from thousands of years trade with Asia and Africa.