Duty cycle would be the average percentage of time that the compressor runs. The compressor on my keezer typically runs around 8-9 minutes per hour, so 9/60 = 15% (and those "on" minutes are in one shot). Like golf, the lower the number the better.
The way I can run all of my coolers (2 fridges and a keezer) and my ferm chamber with tight differentials is by attaching the controller probes to the side of the various vessels (whether kegs or carboys) and insulating them from external influence.
The thermal mass of the beer within provides humongous hysteresis, so the controllers can be set very tight indeed. And, imo, at the end of the brewing day, what you're most interested in is the beer temperature, not the air temperature inside a chamber.
The probe-and-water-bottle is a smaller version of the same idea. But it is smaller, so it will react to thermal changes much quicker than five gallons of beer, with a larger duty cycle (or inversely, a shorter cycle time - more compressor runs per time).
Finally, hanging a probe in free space at the bottom of a keezer seems to be begging for compressor cycling. It has almost no coupling to the beer, and if I was kicking off a primary fermentation I would have no clue what to set the controller to. But I'd sure as heck set the anti-short-cycle mode to something like 15 minutes.
I am a huge fan of tightly-coupled controllers (though a hair-shy of going the thermowell route). I think it allows all kinds of wonderful things, beyond just tight control of a dispensing system.
I brewed up a huge (110 point) imperial stout last Thursday afternoon, knowing I'd be heading out of town to visit grandkids Friday morning - right about when that yeast would be kicking. I put the carboy in my ferm fridge, attached the probe with a 1" thick chunk of closed cell foam over it and pinned them tight with a velcro strap, set the Love TSS2 controller for 65°F with a 1°F differential, attached the 1" ID blow-off I always use regardless, and headed out of town.
Came home Sunday afternoon to see everything purring along nicely, blow-off certainly doing its job but barely any foam hitting the jug. Uncontrolled, that batch would have painted my entire brewery; over-cooled and the yeast could put out undesirable esters; just right and the yeast do their thing in the best possible way with minimal drama.
Whoops! Sorry about the meandering. Finishing off a keg in celebration of getting my taxes filed and it might be getting the better of me...
Cheers!