I run through the radiator to this because, as I understand it, you can't overcool trans fluid.
There are many different opinions on this, mine, for what it's worth, is that you can.
The transmission "cooler" in the radiator is actually a "heat exchanger" - it warms the transmission fluid when it's below the coolant temperature, and also cools it, when it's above the coolant temp.
Think about it - why didn't the factory use a "fluid-to-air" cooler like the one you fitted?
The transmission is more efficient when it's up to operating temperature, so the engineers use a number of tricks to bring it up to operating temp as rapidly as they can, one is to use the "waste heat" from the engine, a second is to disable torque converter lock up when it's cold - the constant "churn" of the unlocked converter helps warm the fluid (at the expense of fuel economy). By the way, care to guess how they determine that the transmission is up to operating temperature? They measure the engine coolant temps - some transmissions have a temperature sensor, but most don't, the ones I've seen that do, are there to sense overheating.
One more thing - if you're going to run both coolers, as you are, run the radiator cooler last - that way you dump the excess transmission heat into the atmosphere rather than the vehicle cooling system, and if you do "over cool", it's warm it back up to the engine operating temperature..