Well, there are two sides to this issue and it's a sticky point for a lot of instructors. I don't teach spin classes, but I did teach regular aerobics for 10 years. When I went through training, we were taught to do the general correction first to the whole group, but if someone was continually doing something incorrectly we should do a more "personal" correction. I would always ask someone permission to correct them, "Do you mind if I touch you?" or "Do you mind if I show you a way to do this that won't hurt you?" I would do it softly and as inconspicuously as I could as I was circulating around the room. People were used to this.
Now, I am not talking about jumping off the bike and grabbing someone's tension knob! That is awful!! But it is an instructor's job to TEACH and sometimes you have to get off the bike to do this. Instructors are not there for their own workouts and sometimes people forget this. When I go to spin class there are always people who are bouncing and bobbing, in the wrong position, etc. and they are rarely corrected. These are things that I would attempt to correct. On the other hand, there are many classes when I am doing something different from the instructor; I don't do jumps and I don't spin at high cadence with no resistance. Sometimes I do a seated climb when others are standing. But, I am not doing something unsafe... I think that's the difference.
Maybe it's because I was a teacher in real life that I had no trouble doing corrections at the gym!