I doubt you would find ATF oil in the radiator. If that was the case, then you could drain the water into the transmission lines.
There are two separate radi cooler systems. I would think a leak would be oil out of the radiator but not mix with the water via Trans.
I would have to see you agreeing that fresh clean oil is gold and not red atf. So, pop the radiator cap off, start the car. If the radiator bubbles, then that is compression loss and it bubbles into the water jacket and not fire off with the kinetic it needs to help fire off fuel.
Take a radiator pressure check to determine a blown head gasket is my guess and not the Trans fluid.