First, NO, it does not use the plugs when the engine is warm (despite the WTS Light).
Next, understand how the relay works. One of the sm terminals will have 12v in it with the key On (BOTH sides will show 12v with the wires connected, only one disconnected) The other wire is connected to the PCM, and controlled, by supplying ground to it.
So, you'll see One big wire with power (the supply) and other has power when the plugs are activated by the PCM (load) and powered independently of the WTS Light. That is, they're ON for Much longer that the light is when cold, and Not ON, even though the light is, when warm. The two small wires are what activate the relay, as current flows through them, and one side is supplied with they key and the other supplies ground, to complete the circuit, through the PCM.
BUT, when testing the sm terminals YOU are supplying that ground path (through the meter or light) just not enough to "flip" the relay. They then both appear to have 12v in them.
For proper testing, remove the small wires so you can see which-is-which. Then, you can supply Real Ground (not through a meter or light) to activate it and see where you have a problem, if any...