The thrust levers definitely have to be at idle before the catches are lifted to shut down the engines. If you reach the stop with them already lifted even partially the balk is still there and you cannot reduce below idle. There have been cases on other types with a similar arrangement of the balk being so worn that it didn't work, but I have never heard of it on a Challenger. Of course CRJs do many, many more sectors in their life so the possibility of a worn out mechanism is greater.
Which brings us to the video posted above. We tried to duplicate this in a 604 sim, and even intentionally could not get the geometry to lift both catches at exactly the right time. It was extremely difficult to do even one, and that required a very unusual seating position for the PM to have their arm in the position shown in the video.