I have installed a new Honeywell thermostat in my apartment. I have a Electo-Hydronic Mark III heating/ac unit made by Snyder General. The problem that I'm having is as follows: When the heat first starts it takes a few minutes, maybe 3-5 for the actual heat pump to kick on. At first its just the fan blowing air. Once the heat pump kick on heat comes out. If the heat shuts off and then comes back on the system restarts and again blows just the fan for the first couple of minutes even the heat is already warmed up. Is there a way to fix this? Is it a problem with my wiring or a problem with the thermostat. I just moved in and don't know how it worked before with the old thermostat so I have nothing to compare it with.

It sounds like everything is working all right. The thermostat does have, and heatpump probably has, compressor protection timers in them so that the compressor doesn't short cycle.