Separate the "hot" side of the outlet. The black (hot) side is controlled individually by the controller. The white side (neutral) should be on all the time (hence joined). Also, you need to get the white into the controller, so it needs to be joined too.
Basically, the circuit is black to white. White (neutral) is always waiting for black (hot) to connect. Black is controlled by the STC-1000. You want to have the controller to turn only one outlet on to cool so you keep the "cold" black side separated from the "heat" black.
The controller decides the temp is too hot, one outlet gets black on (the other remains off). The controller decides too cold, the other outlet get black on (the other remains off). The controller decides the temp is Goldilocks, and both blacks are off.
Does this make sense?
