The temp controller needs to be sampling the temperature of the fermenting beer, not the air temp. You can't just put a carboy in a 60 degree (or what have you) air enviroment and be good. In the beginning, before the yeast really takes off, it will be at or near 60, too cold for most yeasts/recipes. Once it gets going, it will be much more than 60, potentially bad as well. So the controller needs to read the actual fermentation temperature, to keep that in your ideal range.
That is why you need to have the fridge controlled by a separate temperature controller, not the one that is systemic to the fridge.