Lots of things can happen to your body during detox. I have taken the Dr. Natura cleanse, and am pretty sure there would be nothing to worry about regarding the cleanse or ingredients. I have long hair and when I shed more than normal, it's noticable. From time to time dealing with parasites, I have had more than usual come out, but it always seems to go back to normal.
I would try to take your vitamins mid day, after you take the fiber in the am, that way the fiber has already gone through your system and the vitamins can be processed.