Unless yours is wired completely different, your inverter should have a "cross over" switch that automatically "switches" the source of power originating from the battery (12v DC) to shore power (120v AC) as soon as you plug your camper into shore power. The output from the inverter is 120v AC, same as household power, but the cross over switch knows when to switch the source of power from household to the inverter.
It is possible the refrigerator is wired directly to the output of the inverter and does not use a transfer switch at all. Either way, the output of the inverter will go through a breaker or fuse of some sort. That may be in your house breaker box, or somewhere else. I found an entire second set of fuses under the floor of my Fifth Wheel when I removed the wall from inside the overhang pass-through. I'm assuming those are for the inverter and everything the inverter powers.
Below are two screen shots of the wiring diagram for my inverter. As you can see, these diagrams are using a transfer switch. But the output from the transfer switch is still going through fuses somewhere.
FYI, I also have a Samsung and I've read instruction till I'm blue in the face, and even called Samsung direct as asked how to turn the refrigerator off - completely. Answer? You can't. The only option is to unplug them. You can turn off the cooling unit, but there is still power to the light inside. To completely turn it off, kill the power.
If yours is wired directly to the inverter, all you need to do to turn it completely off, is to simply turn the inverter off. Try turning the inverter completely off and see if the refrigerator turns completely off, lights and all. If it doesn't, then the power line running to it is on a transfer switch, switching from battery to shore power. (provided your camper is plugged into shore power).
Crossover - Transfer switch output is pathed to a secondary sub panel of breakers or fuses:

Crossover - Transfer switch output is not pathed to a secondary sub panel of breakers or fuses, instead is wired directly into a wall socket.
