I agree with others that something is not compatible between the two. Ill give you something that is weird too and others probably have this feature on their too but my T-stat also has an auto mode for the heat and cool side too. When mine is in auto mode on the HVAC side it will do what ever it needs to keep the set temp. It's screwed up when the A/C is on upstairs and the furnace is running at the same time.:S
My wife has problems working the t-stat and sometimes turns the auto on. Sitting there watching tv or something and the rv gets cooled out and the air kicks off and then a few seconds later the furnace will fire. HAHA!!! Makes no sense to me. LOL!