I tried reproducing this with my setup, but I'm not seeing it. The only way I could get the cabinet on/off state to have any change in sound through my external amp was if I set the Amp Out Source to Main Out instead of PreCab/IR. When I have Amp Out Source set to PreCab/IR, turning the cabinet block on and off did not change the sound coming out of my amp at all.
I know these are probably dumb questions, but are you sure you're using the Amp Out jack for the cable between the POD and your amp? If that is setup correctly, then are you turning off your monitor speakers so you only hear what's coming out of your amp?