My thermostat seems to not be following the program and comes on earlier than it should.

Your thermostat may be entering Adaptive Recovery Mode. Adaptive Recovery Mode is a feature that attempts to achieve your set-point temperature by the time you desire. Because of this, your heat cycle might start up to 2 hours early and your cool cycle might start up to 3 hours early. This all depends on how many degrees of recovery is needed. Many newer Braeburn models allow you to turn this feature off in the User Settings mode. Please see your users manual.