My programmable thermostat will turn the heat on before and after the set temperature.Is this normal? Example, thermostat is set at 22 degrees, sometimes the thermostat turns heat on at 22.2degrees or sometimes it will not turn heat on till 21.6 degrees.

Yes normal. There is a degree of differential built into the thermostat. Other wise it would be turning off and on too much to quick and damage the equiptment.

My programable thermostat will turn the heat on before and after the set temperature.Is this normal? Example, thermostat is set at 22 degrees, sometimes the thermostat turns heat on at 22.2degrees or sometimes it will not turn heat on till 21.6 degrees.
So it is normal for a thermostat to turn the heat on at a higher temp than what it is set at?

Just what I said in my last post. Thermostats are not completely accurate. There is a differential allowed. So it is possible the thermostat could turn the heat on a degree to soon or to late. Also unless you have a professional digital hand held thermostat that is calibrated every year at the factory you are using just another thermostat to check the temperature and the one you are using to check your heat thermostat could also be not accurate. NOTE: the thermostat display on heating thermostats are known to be inaccurate from the factory. I have seen thermostats that were much worse that yours.