I don't if anyone has done proper destructive laboratory analysis of these famous red finishes. Jack's famous rifle with the much beloved red finish used polyurethane varnish colored with dyes of some kind.
I have built violins and worked in violin shops and most instruments have a very soft finish that will not take much abuse. I'm not sure, just because it seems to be a colored varnish finish, that "violin finish" is the correct term, and people may be allowing tunnel vision to take them down the wrong path. It's not difficult to use alkanet root or dragon's blood to color oil or spirits and make finishing products from them.
This is not my area - I speak Virginian - but still, the phrase violin finish is used and I think it is possibly leading people astray. But perhaps I'm wrong - perhaps there is a known connection between these makers and a particular finish technique similar enough to instrument finishes to merit the term. Sorta kinda doubt it, though.