Looking at the pilot training manual for a CJ2 525A, section 12 is pressurization and this citation has 3 modes: AUTO, MANUAL and ISOBARIC.
In AUTO you select the destination elevation prior to taxi and the system will automagically generate a schedule of pressure changes so you arrive at your destination completely depressurized.
If the switch is in the MANUAL position you must control the pressure with the manual toggle valve (a red cherry picker knob.)
If while in AUTO there is an interruption of data the system will automagically switch from AUTO to ISOBARIC control. You will have to set the desired cruising altitude (in FL.) The controller uses the cruising altitude specified to control cabin rate of pressure change to maintain optimal differential pressure. You can flipflop to display cabin altitude and set that and the controller will maintain the specified cabin altitude.
So I guess I was wrong, it seems that most of the time the computer is maintaining a differential of pressure automatically -- and then if the computer fails it reverts to isobaric control where you have to enter some of the data in for it. Atleast on this aircraft.