Thanks to -d the client will start a new session (dispatch the job), but it won't attach the new session to the terminal. The client won't put you into the session, it will exit almost immediately, this will make the shell interpreting the script continue. (Note nohup is similar in this matter: it exits after setting up a job.)
This means most likely you don't need to worry. If you start your job in tmux in the right way (described above) and if you don't create additional panes or windows in the session, then the session will exit automatically when the job is done. Compare this anotherother answer of mine.