Your fridge is likely new enough that it has a way to select Gas, AC or Auto. On Gas it uses 12v and Propane. On AC it uses 110v AC and 12v DC. Most travel with the fridge in Gas/Auto mode using propane. If in Auto mode, and the generator is running, AC will be the main power source, with some 12v DC for the control side.
Propane should be off when refueling. Also, some tunnels require propane to be turned off.
Be careful with how level you are when parked for any extended period of time. The fridge likely wants to be within 3 degrees of level.
2016 Fleetwood Bounder 33C. Towing 2017 Jeep Wrangler Unlimited.