[old_tv_nut]

Removable mounting bands (as opposed to the permanent compression bands that were permanently attached to some much later tube types) should be tightened only enough to hold the tube in place.
Edit: the mount should be designed and perhaps have cushioning so that excess force is not applied to the tube even though screws are firmly tightened. If the tape you applied is the only cushioning, then the caution about overtightening applies.