Can’t turn off power to thermostat
BRHANS is absolutely right. Use a multi-meter to check for actual "voltage". 24 volts A/C is the minimum voltage you should have. You said you have two systems. By chance do you have a zone control board for any other zones?? sometimes they have their own transformer and a separate control wiring. If you do NOT have a zone control board, get a multi-meter that can do LOW A/C voltage and verify the voltage. Check voltage at "R" to "C". with power ON you should have 24v A/C. If you still have voltage with the system off, you will have to check power at the HVAC equipment. I'm not sure the age of your furnace/ air handler, but some of the older equipment has a separate Transformer that runs the low voltage side only. This may have a separate power source as well. ( not very common) but I have seen this situation in the past.
 Hope this helps. and good luck to you.