The website for the card clearly shows you will still get 1 elite night per $3k for the Premier credit card (but not premier plus). I tried to copy/paste it here but the stupid website won't let me. I think the "on or before March 1" language is meant to imply you cannot get 15 nights from the Marriott card PLUS 15 (or whatever) nights from ANOTHER credit card.
Marriott Rewards Credit Cards