It's the other way around. The fan clutch is the main fan at idle and low speeds. The aux fan is....auxiliary. Only kicks in when the fan clutch can't keep up and when AC is on.The fan clutch doesn't do the main portion of the cooling. It's the electric aux fan that does the vast majority of the cooling when stationary.
What coolant are you using? And mix ratio?
Which thermostat did you install? It could possibly be defective. They usually fail open, but I've seen a couple fail closed and raise both temps like in your situation.
Might want to try doing a combustion leak test.