My guess is that you have some kind of local ground loop, and the "weird pulsing" is an effect operating on the hum.
If this is the case the solution is at your end.
See if it occurs with your pedals in relay bypass, and try disconnecting things until it goes away – this may give you some clues.
My assumption is a grounding problem. I didn’t think about switching to relay. I’ll try that in the morning and post the results.