Over population and dysfunctional governments leads to migration. Climate change is not a significant factor in Africa or South America. These pressures would be happening even if climate change was not an issue. As I said, climate change and migration is most a political tool used by political actors to push an agenda that has little to do with climate change.
Did I not mention population? The consequences of multiple crop failures due to climate are what drive migration. They also drive political instability. I'm surprised you would think they are unrelated issues.