In the end, some companies do it one way, some do it the other way. Both ways have been shown to be acceptable to the FAA. Depending where you are, that's the way you do it, regardless of your personal preference. If and when you change employers, if they do it differently than what you are used to, you adapt or you move on.
All that said, at Delta the PM makes changes with the AP off, as directed by the PF. PF makes changes with the AP on, or can direct the PM to make changes during high work loads (below 10K.) If you come here, that's how you do it. Please don't tell us how you did it at your other airline and how it was so much better. Don't be "that" guy.