How do you justify THEM surviving in 120+ degree temperatures in an african reserve?
Creative freedom, in the words of KP. Its somewhat passable because, you know, these animals are still alive. And have not been dead. For thousands of years.
As for the South American ancients, moving past the rudimentary temperature differences, the entire global ecology is vastly different than it was 10 thousand years ago. Different seasonal shifts and life forms. Forget being outmatched by a lion or tiger, a terror bird would choke on the new atmospheric conditions or die of sickness because of the new kinds of bacteria and viruses in modern days.