The configuration writes the profiles, the bridge executes them, there is no relation to the default X-Plane controls, they are completely unaware of each other.
I think there's something not right with the configuration. Maybe a conflict between the bridge and the default controls. Or maybe something needs updating in the profile.
My profile is very simple. It only covers the autopilot controls and lights, no other buttons or axis, they can be done with X-Plane (AirbusFTW had other ideas, so there's alternatives :)). I'm a firm believe in keeping my sim setup as simple as possible. (I don't actually use my profile anymore, I have another autopilot control.) However, I did generate a summary document: https://github.com/pilsnerish/Honeycomb-Profiles/blob/main/CL-650.txt.
I think you may be confusing my profile with another, AirbusFTW's I would guess. However, that sounds like the behaviour I would expect as that matches the real plane's fuel shutoff function. Again, it is not necessary to use the bridge to achieve this.