"Are Asians and Africans different animals with different ancestors then? Or did evolution run a parallel path on different continents?"
Not really. As you may note, Africa and Asia are connected via land. I don't see the problem with migration between the two.
It seems unlikely to me that homo sapiens evolved simultaneously in two places, so a single place is much more likely, IMO.
So your "Both are true, but at different times." referred to South American population, not the question of where life began Africa or Asia?
But you forget that the founder of your faith believed that Africans were not as fully evolved as Europeans.