My miles on CI posted to DL about 2 weeks after the flight. The ticket was CI, not DL, and I did not get MQMs (didn't expect to, but can always hope for a mistake).
My guess is the delay is probably a fixed delay plus a monthly cycle from what I have heard, so give them well over a month before you bother with a call.
Somewhat OT here but I'll ask anyway, is it possible to get the DL ticket on CI flights at about the same price as CI tickets? Whenever I search there is a huge difference. Would love to get the MQMs if I can find the DL biz class at under $2000.