I still don't agree with the logic. Let us take two cases: one person is vaccinated, and the other isn't. In both cases, when they contract the disease, their bodies are going to produce antibodies to fight the pathogen. So, if the pathogen mutates, it could very well do that in both cases. The difference is that in the vaccinated person, the pathogen introduced in the vaccine is inert and so doesn't cause the infection, and so the body is pre-prepared to fight it IF the same strain enters the system at a later point of time. In the unvaccinated person however, it takes some time for the body to prepare its defenses and if the pathogen is potent enough, it can simply swamp the body's immune system, and then unless the person takes some drugs, s/he is in for trouble. I'm thus somewhat skeptical that a vaccine can by itself cause a mutation in a pathogen.
Now, in the case of TB, there are plenty of cases where the patients have to take drugs when they contract the disease. Hence, the bacterium evolved to develop resistance to the drugs used to kill it. I don't think the bacterium evolved because of the existence of the vaccine. Then again, I'm no medical expert, and so if there is proof somewhere that this can happen, I'll gladly accept that I am mistaken.