I have found an inaccurate note in the Cubase 11 documentation (link) which applies also to Cubase 10.5. It says:
“Moving chord symbols in the staff only affects the display. The position of the chords on the chord track remains unaffected”
This is not true. To leave the position of the chords on the chord track unaffected, you must use the Layout Tool (you can’t reposition the chords using any tool).
The following note should also be included:
Chords from the chord track can be copied to any score layout. This lets the user to make adjustments that don’t interfere with how chords look like in other layouts.