It does kick in quickly with regard to MP but takes reservations about 5 days or so to take hold. Their computers don't talk to one another very often this way, it seems.

I saw my new 1K status on the website the next day after the flight, but when I called to make reservations it was a hassle because they didn't "see" the status and it took a number of days.

Same thing happened when I became a 1P.