I was never made to vomit, and I can't imagine any decent therapist making you do anything you are not willing to do. The vomiting episode I had was not due to therapy - I had a stomach virus. Which led me to start therapy again. if I gave the impression that I was made to vomit, I am so sorry!
However, it has been my (tentative) goal in past therapy, and current therapy, to be able to vomit, and to possibly incorporate the actual act into therapy, once/if I feel ready to. I feel that the best way to show myself that I can do it is to do it, but that is certainly a distant goal. I've never heard of any therapist saying that it is necessary to vomit to get over the phobia; my goal has been to get to the point where if I need to vomit, and my body is going to do it no matter what my mind wants, I can do so with less panic than I currrently experience. An equal goal is to be able to live without the constant fear of it happening, with everything being viewed as something that could lead to it.