Furnace Displays Heat Pump mode when AC is running
The outside unit is a compressor , the difference between a heat pump in heating and cooling is the Direction of the refrigerant flow. So for a single fuel heat pump to cool it may well be running in stage 1 but a reversing valve has altered the flow. If you have a dual fuel system then in heating a choice is made based on the temp which one to run. Your thermostat probably doesn’t have all the functionality or was not fully programmed but to get cooling the outside unit needs to run and the reversing valves are set to cool. 
If it’s cooling everything is fine the thermostat is commanding the compressor on and it has the reversing valve in the correct position.