Right on, first question, what is the ambient temperature in the area where the refrigerator is located? If it's less than your setpoint you're going to need a heatsource as well and probably a dual stage controller.
Second thing, maybe you set the temp to 65, and maybe the ranco shut the fridge off when the probe hit 65, but there is usually some latent cooling effect, i.e. the temperature continues to drop even after the refrigerator shuts off. So it could have continued to drop to 61.