The fridge will cycle just like the one in your house. If it did not, it would constantly get colder and colder and colder and colder. They run on a thermostat and once they reach the temperature setting will turn off. It usually takes 12-24 hours to cool a refrigerator in an RV if it's not been turned on and already cold. If you put a bottle of ketchup and a glass of water in your chilled household refrigerator, would it cycle on? Probably not. It will cycle on eventually though.
I think your refrigerator is perfectly normal. Keep that water in the freezer over night and I bet it's frozen in the morning (if not sooner).