In the above picture I screwed in the ground (green) wire of the main cord to the ground leg of the outlet. I've also attached one 4" wire to the "left" leg of the outlet.
I'm continuing the wiring job by attaching the 1/4" ends of the 4" wires to the controller. I tightened each one snugly into the controller but did not overtighten.
I intentionally broke the "right" side connector between the upper and lower portions of the outlet, so that one will operate for hot, and the other for cold.
That's the final wiring. Putting it all together
I've wired the 2 wires for the sensor, and routed them through the same hole as the main cord. I also made a loop around the main cord to prevent it from being yanked out.
Here, I've screwed down the electrical outlet to the box, but not tight to leave a little bit of wiggle room.
I then gently tucked the wires behind the electrical outlet, and put the controller and faceplate on top of the box to try it out.
I adjusted the outlet, tightened it down, and put the faceplate on top of the box, and used 2 of the screws to hold down the face plate. Since the faceplate screws into the inserts (and NOT the box), there's nothing for the top screws to go into, so I just left them out. For looks, you could glue the remaining 2 screws into the outlet, but I'm all about functionality over looks.
That's the final product. Looks decent, works great.
The back of the box can be left as is, as there are no wires that show metal.
Or, you can put electrical tape to cover the holes.... Or whatever other material you so choose.