Heat Pumps and Electric Heating - Aux Heat

Heat pump with oil furnace backup. There is a temperature sensor outside that cuts out heat pump and runs on aux heat at a certain temperature.The problem is when this is activated when furnace fan starts aux heat is supposed to come on immediately but it doesnt it only comes on when temperature of house drops. Is this a thermostat problem or is it wiring to relays at furnace. THANKS IN ADVANCE.

Im lost??? With the ODT it should say if the pump runs or the oil furnace runs to heat the home. Now when the oil comes on it will run till a set temp in the furnace then the blower should come on. The fan should not run till the furnace is warm. When on H/P the fan should come on when the unit calls for heat or AC. Is this a new set up or did this just start in a old set up???

This is anew setup .What happen was for some reason my heat pump would not run.So a hvac contractor checked it and determined that the heat pump board that was screwed on the furnace was faulty.So instead of putting another board he replaced it with relay contactors and that is when it started doing this.Also i noticed that when thermostat calls for help for heat because heat pump cant keep up in colder weather the furnace and heat pump keep running at same time.THANKS IN ADVANCE

This is anew setup .What happen was for some reason my heat pump would not run.So a hvac contractor checked it and determined that the heat pump board that was screwed on the furnace was faulty.So instead of putting another board he replaced it with relay contactors and that is when it started doing this.Also i noticed that when thermostat calls for help for heat because heat pump cant keep up in colder weather the furnace and heat pump keep running at same time.THANKS IN ADVANCEABOUT FURNACE HEATING UP BEFORE FAN YES IT WILL DO THAT WHEN SYSTEM SET IN EMERGENCY MODE AND RUNNING ONLY ON OIL FURNACE.