No Autothrottle on the CJ. Any speeds in the FMS are only for reference.
In the real airplane you can sync FLC to the climb or descent speed profiles in the FMS using VNAV (depicted as VFLC). But even then it doesn’t adjust throttle. Only changes pitch to try to maintain a speed.
There is a guide to programming the FMS linked below. (But it was written prior to all these improvements)
https://forums.flightsimulator.com/t/how-to-citation-cj4-fms-programming-guide/124457/2