I am going to add my thoughts but would strongly advise that you get confirmation from others to confirm for sure. Also, I am assuming you are talking about the enrollment message when you speak of the "welcome message":

My understanding of this functionality is that the enrollment message will only be sent to newly assigned users to the program, including users assigned via dynamic audience, and would NOT be sent to users that were assigned to the program before the enrollment message existed. This seems to be in alignment with your testing and expected behavior.

I think it would be great if others could confirm this as well, but I think that your line of thinking is correct.

Now on the other hand, what happens if users are assigned via dynamic audience, then remove for some reason, then re-assigned back to the same program later? In this case I think they receive the enrollment message again.

Jamie