Tuning up should indeed be done off-stage. There's a problem though if on-stage is significantly warmer: when doing a zoom session during the winter, I've found it best to tune up with the clip-on, then let the guitar warm up nearer the fire for half an hour before doing a final tune-up (usually by ear).

This temperature problem seems worse with (*ghasp*) the banjo*, which, come to think, might account for some of the jokes about tuning them up. But if all else fails, I could always throw caution to the winds and the banjo on the fire.

* Other problem instruments are available.