So the goal of the adenovirus is to introduce the broadly neutralizing antibody into T cell lines. These are the immune cells that are going to be ultimately fighting HIV infection, but they lack the right antibodies. In the normal situation, your body raises antibodies, but they cannot bind to the right spot on the virus envelope. Instead, they bind to a spot that the virus naturally varies, and the virus escapes via mutation (i.e., mutated virus replicates, other virus doesn't). In the new situation, the adenovirus provides an antibody that is better, which binds a spot on Env that the virus needs (so virus with mutation at this spot replicate poorly).
So muscle and heart cells are likely not getting the vector, nor would they be expressing antibodies. Similarly, your body wont continue to raise the antibody if the infection is gone (it will not be ad infinitum).
This is my understanding ... perhaps others could add key points.