I have hooked up the new Hunter thermostat replacing a Rheem 41-20804-15. The system works but the aux heat stays on the whole time the heat pump is on. Shouldn't the heat pump comressor work for a while by itself before turning on the aux heat?

I did hook up the old termial (W2 and E) both to the Aux connection on the new one

Sounds like you need to carefully look at the wiring instructions again,, although the Hunter tstat (most) are junk if you get lucky and get it to working,it won`t last long,, take it back now whiles its still new