A detached hair found on the body generally does not invalidate immersion since the water moves around it when you are in the mikveh. However, it is possible that the mikveh attendant recommended you immerse one more time in order to have one immersion where you are positive that there are no barriers at all, even ones that would not invalidate the immersion. While the current practice is to immerse more than once, in actuality one immersion suffices to make you tehorah. One of the reasons we immerse more than once is to ensure that at least one immersion will be perfect.

Additionally, if you did your preparations and inspection right before immersion, we can assume that the hair was not there when you immersed, and you only stepped on it after immersion. In that case, you would not need to immerse again. However, as we stated above, it is possible that the mikveh attendant wanted you to immerse one more time as a precaution – especially since you were still there in the mikveh. If you had already gone home, you would not have had to return to immerse.