I got a Delta Platinum last month and my sign-up bonus posted 2 days after I hit the threshold. I managed to hit $25k and Delta recognized the MQD waiver about two days later (and it looks to me like they update the totals spend counter every 7 days?) but I don't have the MQM yet. I couldn't find anything on either site about what schedule they'll arrive on.
Kind of hoping they show up soon as it will push me from Gold to Platinum on a trip where it looks like that will matter (not to mention the miles earning difference), but I also saw some post that implied they only show up after statements close. That would be unfortunate since that's probably too late for a second long-haul trip.