Air temperature is going to fluctuate very quickly. The walls will stay cold after the freezer shuts off, cooling air near the sides and causing convection currents that show fluctuations on your probe reading. Even with a fan to even things out, you're never going to be able to keep the air temperature around 63 without cycling the freezer on and off constantly, and this will break your freezer pretty quickly.
You don't care about air temperature; you want to maintain the temperature of your beer, so tape the probe to the side of your carboy (or use a thermowell). 5 gallons of liquid has a lot more thermal mass, so the freezer will run for longer periods of time and then shut off for longer, and your beer temperature should only fluctuate 1 or 2 degrees.
+1 I've been running an A419 for several years. By the time it cycles off, my 3.5 cu ft. chest freezer will cool down at least five degrees more, but it warms back up fairly quickly. However, like clock work, a fermenter will run about a degree or so above my SP (depending on the vigor of the fermentation). I dangle the controller probe about an 1" or less from the fermenter.
I learned from experience, though. You don't want to run a freezer with a controller with a probe in a thermowell. That will cause severe over-run. I do use a thermowell, but just to run a thermometer probe down to check the beer's temperature. The controller-in-the-thermowell setup is good if you are running a fermenter heater, though. Holds mine almost constant.