This behavior is generally indicative of being low on refrigerant.
Those cans with gauges cause lots of problems, it is best to use a manifold to introduce refrigerant by weight after discharging and vacuuming the system.
James on these k2's if the temperature sensor is goofy it "can" cause the fans to run after the vehicle is shut off (which yes that can be commanded to do under normal operation) if the temperature is high.
but if the sensor is reading incorrectly it also makes it happen when it shouldn't, for instance if it was going to happen to anyone (from being hot after shut off) it would be me and it never has and it certainly wouldn't do it all the time. the erratic ac operation is also symptom of the temp sensor being goofy also it has been reported a number of times.
1. fans running after engine off
2. fans running high speed at cold start or constantly throughout the day
3. error messages saying engine hot ac turned off (when the engine is not hot, and/or gauge says normal)
4. incorrect temperature gauge readings, too cold, too hot, gauge pegged either way
the temp sensor's go goofy and the thermostats get stuck or do not operate correctly also.
it very could still be low refrigerant, but that wouldn't cause the fans to run after the engine is shut off
there is some low-key association with the temp sensor/fans/ac, I think it has to hit a certain parameter to throw a code, like if the temp sensor fails x amount of times in a row
some people have also reported disconnecting the battery sometimes corrects it for a week or two, then it fails again. that tells me these temp sensor are apparently borderline when they go bad.