An option is to duplicate the video and put the second right under the first so that the precisely overlap. The video on the lower track is the one that you track the front of the shirt and put the logo in. After this you gradually increase the opacity of the second clip, so that it will become more and more visible, including the logo. Because the top video is the same and the only difference is the logo-picture, viewers will see that the logo appears.
mind you: when you talk about a person turning around, it will not be so trivial to make the logo turning in the same fashion and speed.