It depends a bit on how you define immigration. Is what the Spaniards and English did to the Americas immigration or something else?
If the influx of a different culture is so big that it displaces you and your children like it did to the Native Americans, then I understand that you'd want to stop it.
I could be wrong, but to me those words describe the initial phase. Once established as a society, the rest involves people moving into this society, which I would call immigration.
That's how I think about it too. I guess the original description was a bit vague, what they did to the americas. It includes both. First invasion, then immigration.