Do vitamin tablets actually work?

Yes but it depends on the product as some are cheap and aren't going to absorb well. There is a simple vinegar test you can try out (see video below) to see if your supplement breaks down.

I've corrected a very long list of deficiency states, many of them severe deficiencies, taking vitamin and mineral supplements. I have autoimmune pernicious anaemia (unable to absorb vitamin B12 in the gut) and take 2000 mcg daily of sublingual (under the tongue) B12 spray for that.

Vitamin Test??:
https://www.youtube.com/watch?v=QseivezW7uQ

They provide vitamins but unless you have a deficiency I cannot say they do anything.

They do work once you have a deficiency or an illness example if you have anemia you would need extra Vitamin b12 and persons who consume more Vitamin c is less likely to get a cold than those who don't .