I recently purchased a 5 sq ft chest freezer and A419 Johnson temp control for fermenting my beer. I hooked everything up with a Setpoint temp of 63 degrees and a Differential of 1 degree to test it out. The freezer kicks on just as the A419 moves to 65 degrees as expected, but doesn't kick off until the freezer cools to around 55 degrees (or sometimes cooler). The reason appears to be because the A419 thermostat is slow to react to the temp change inside the freezer. The freezer runs for about 2 minutes before the A419 finally drops to 61 degrees and cuts off. But after the freezer cuts off the temp reading on the A419 continues to drop as it "catches up" to the actual change in temp within the freezer. Is this normal? Should I expect a true 10-12 degree differential because of a slow-reacting thermostat or do I have a defaulting A419?
This web page mentions the device has an "Adjustable Anti-Short Cycle Delay" that controls a time delay that avoids rapid on-off cycles of whatever it is you are controlling. Could it be this?
If not, do a test: Dip the probe in boiling water and see what the screen displays. If there is a long delay before the display shows the correct temp (100C) then I think it's faulty. There should not such a big delay.
PID controllers are designed to avoid this problem of over/undershoot. But a 12deg overshoot is a bit much in my opinion.
I'm using my A419 to chill beer, not control fermentation temperature, but I found dropping the probe into an improvised well (in my case an empty plastic quart bottle) stabilized the temperature. If you do try a well of some sort, make sure the probe can't come into contact with liquid: the cable is waterproof or at least water-resistant, the probe isn't.
It may be that 63 degrees is too close to your ambient temperature for the thermostat to settle down properly. I wouldn't know about that, since mine is set to 34 F.