This is explained in the GSX main manual, and in much greater detail in the PaintKit manual.
The selection of service vehicles is NOT dependent on the atc_parking_code of the airplane you are flying! What affects the selection of the handing company, is a *scoring* system, calculated using the ICAO code of the airport, matched against the couatl.icaoprefixes of the *vehicle*, which gets a score depending how many letters are matched AND it gets an *additional* boost to the score, in case the the parking code of the *parking* matches the vehicle.
The atc_parking_code of the user airplane, instead, affects the selection of the livery of the ULD containers ONLY.
The reasoning behind this, is that services vehicles companies are local to the airport, so are not affected by the user airplane (if I land my Alitalia plane at JFK, I doubt I'll ever find any Alitalia crew there), but the ULD containers loaded ARE dependent by the airline of my own plane.
Of course, there are fallbacks in place so, if the airplane doesn't have any atc_parking_code, the ULDs will be selected just like the vehicles, using the icao+parking selection score.