the difference between aux heat and emergency heat is that emergency heat forces the heat pump off and designates the aux heat as primary heat source while in this mode. when a zone board receives a mode signal change, it discriminates as to what runs and time delay is a normal part of the process, as mentioned. the purpose of emergency heat is to switch to aux heat in the event the heat pump is not working. otherwise, if the heat pump is functional and working properly, aux heat is turned on as second stage to add heat if the heat pump needs help to maintain setpoint temperature. in that case, the addition of aux heat should be seamless without delay. the board receives a secondary signal and simply switches on the aux heat source to further warm the air. if you want it to be warmer, raise the setpoint rather than turning on emergency heat. only do that in the event of the emergency (heat pump failure). then call for service.