They are called dual fuel the out side units operate on exterior temp and thru the add on box shifts auto to the gas furnace when the exterior temps drop to the desired setting. I have a propane furnace for my heat pump but do not have the add on box came factory wired with a external temp sensor.
Your furnace was most likely installed with a standard A/C and the owner got sold a heat pump at a later date. Did the date of MFG match or were they different.
I can not tell from afar there are so many variations on how a system can be wired with different controls to perform different functions.
The emergency on the stat is to be used if the outside unit fails the normal operation can and does bring the gas unit on if needed and during the defrost defrost cycle. Did you try to run the stat up 3 or 4 degrees above its setting and see if the gas kicks in. You may have a improperly installed stat but on the other hand depending on its wiring if the outside unit failed the gas furnace auto picks up the load. Sorry not much help from afar just to many variables
Did you try to run in normal heat and just move the stat 1 degree to see if the heat pump operated with out the gas furnace.
It is possible someone just using the heat pump as standard A/C one could tell this by the amount of control wires traveling to the exterior unit from the furnace. It there are only two low voltage wires it is for cooling only if more than two wires it is used as a heat pump