This kind of thing has happened to me, and it always ended up being a simple fix.
First: Did you wire it yourself? If you did double check that.
Also try adjusting the differential. if its +/- 5 and set for 65 F, the fridge won't come on until it hits 71 F (Cooling) and the same would run true with the heating.
I don't have a 2 stage, I use multiple 1 stages. But have you tried both plugs? Its my understanding that one plug will be heating and one for cooling. I don't mean to insult, but I know I do things like this all the time
Good luck!