The compressor should have cycled with the fan. If it didn't the unit worked like a refrigerator. Try again with the fan on all the time like you thought. If it ices up again make sure the filter is clean (I know new RV but still, it's happened), and there are no obstructions to the air going into and out of the unit. Our AC unit has a sliding grate on the discharge side that allows all the air to go into the living room or close it and the air goes through the ducts to the bedroom and front of the RV. If there is a blockage (vents closed in other parts of the RV for instance) that would limit the air flow and cause icing.
Good luck.