I am not an Electrician but I wounder if outlets are ever split and fed by two different branch circuits.
I saw this on a house we had in Michigan. Was done for a kitchen outlet. Maybe to power two fry pans(?).
It should be "relatively" easy to determine.
Plug a night-light (or some other tester) into each of the two sockets of the duplex outlet.
Ony by one, flip off breakers, and see what happens. If both lights go out at the same time, they are on the same breaker. If they go off separately, they are on different breakers, which *might* be on different phases.
Try plugging both the CM15A and the chime module into the same power strip (or even an extension cord with multiple sockets at the end), plugged into one of those outlets, and see if you can control the chime. Try the same thing in the other outlet.