Wall warts.
Small power supplies you plug into the wall. Like one you may see on a computer or powering other small devices.
The external power supply for the SC1200 Security Console and MT12A,MT13A and MT14A Mini Timer could be called a wall wart. Though they are special as it also has the X10 power line transmitter in it.
If moving the CM15A to the other phase and the ones not working now work. You maybe correct in the phase coupling issue. Another clue would be the ones that worked before do not or are spotty.
Did you check your breaker box? If the XPCP was installed using the instructions. Each of the two line connections would be through a breaker and both neutral wires on the Neutral buss.