Just the way it should be! Though at least on the Ford, there was a bit of a whine when that electric AC compressor would really get spinning.Not sure yet with that. I've done the remote climate control a few times from my phone and I know a few times at least the engine never came on (just ate away battery power). What's nice about it is that it runs the system and doesn't run anything else, like headlights, to let others know that your car is running. Pretty sneaky!
I'd guess if you just did a remote climate control it would fire up the ICE if it's too cold out. But you should have settings somewhere so that you can say you want to have the car charged and warm at like 7AM, right? That's the one that I wouldn't normally think would fire up the ICE but I'm not sure. And/or maybe if you did the remote climate control while plugged in...