Sorry for the late response.
I am a mechanic and avionics technician on r/w CRJ-200s which have very similar systems to the CL650, although the CRJ uses the older Collins Proline 4. rather than the newer Proline 21 on the 650. But, the operating principles are the same.
The flight director shows steering commands coming from the autopilot.
However, when the aircraft is flying an ILS approach in “green needles” the steering commands for both the pitch and roll servos are not coming from the autopilot’s command logic. Instead, the aircraft (when the autopilot is engaged in approach mode) is being steered directly by localizer and glideslope deviation outputs of the VIR-432 Nav radio. In this mode, the autopilot flight director is only in a passive “monitoring” state. The Nav radio itself is “doing the driving”.
The Nav radio responds much more quickly to any deviation from the localizer or glideslope than the flight director - especially in the latter stages of the approach.
In fact, on some Boeing airliners, the SOP is to turn the flight director completely off once established on an ILS, as the flight director command bars can be distracting in this scenario because of their slower response to any deviation from the localizer or glideslope.