Heat always flows towards cold (less heat). Theoretically both fluids are the same temperature before start up. Both start flowing immediately. The coolant is going to start getting warm first, as it's cooling combustion. The ATF is just heat by friction. Since the coolant gets hot faster, the heat will flow into the ATF at the transmission cooler.
But the coolant is cold in the rad until the thermostat opens. After it opens there will be heat flow from coolant to ATF but for the initial period the ATF will be giving up its heat (no matter how marginal) to the coolant rad.
Oil cooler incorporated into coolant radiator. Brit speak that never made it across the Atlantic!Saddle cooler?
210F is a little high, are you sure it's not just your gauge?
Possibly a touch high and/or inaccurate gauge but as it is just on the cusp of the temp water boils at at atmo pressure and is in a sealed (pressurised) system designed to avoid boiling I'm not overly concerned.
The transmission cooler is on the cool side of the radiator, even if engine temperature (taken at the head) is 210F, that side of the radiator should be quite a bit less.
If it left the rad at 85C (185F) then that's still on the high side for cooling ATF - no?