I worked in a radiator shop many years ago rebuilding radiators. Virtually every radiator made for a vehicle with an automatic transmission has an intregal transmission cooler built into the radiator. Check any vehicle with an automatic transmission, besides the radiator hoses there will be 2 metal lines connected to the radiator too. Those transfer the tranny fluid between the transmission and the cooler in the radiator. Those tubes can plainly be seen in the picture in the link.
HowStuffWorks "How Car Cooling Systems Work"
In the case with the OP, if that tranny cooler was to leak, because the transmission has greater working pressure than the engine coolant system, transmission fluid will be forced into the coolant system. But when the vehicle is turned off, the coolant then could be drawn back into the transmission as everything cools. It doesn't take much for this to happen, just a small pin hole leak. Engine coolant will destroy a transmission in short order. The OP also stated the radiator was tested and found to be good. This can happen if the testing was done with air. The radiator hose fittings are plugged and about 15 psi (about normal radiator coolant pressure) air is pumped through the cap fitting. The radiator is lowered into a large tank of water and one looks for air bubbles. Better radiator shops will use test fluid that is black light sensitive and heated to 175 degrees. This is allowed to flow through the radiator for about 10 minutes then a black light is used to check for leaks. When I was involved in auto racing, I had access to such a system and found it to be a much better way to check a radiator than using air. This type of testing would also show if the internal tranny cooler had a temperature sensitive leak too.