It is possible for a Citation jet to not have an APU, two of them that come to mind are the CJ2 and CJ3 aircraft. An aircraft with an APU can have an independent air conditioning system or not, it just depends on the installation and manufacturer. Some airframe manufacturers use engine (or APU) bleed air to condition the cabin air temperature. Something like an APU would have overhaul limits similar to an engine, propeller, or a combustion heater like in smaller aircraft. Anything with a life limit would have to be tracked, so that could be individual components of a larger system, such as the starter/generator of an APU, or a compressor motor of an air conditioning system. I think what you're seeing is a coincidence.