In my experience Membership Rewards points post when the PDF version of the next statement is available online. For example, if the Closing Date is March 19, the new online statement will appear on the 20th, the PDF statement and points earned the previous statement should appear on the 21st.
This makes sense. They post when the cycle in which you pay the bill for them closes. The reason it differs for MR versus the SPG card or any of the others is that MR will actually not give you the points if you're late paying (though you can buy them back within the first month). On the flip side, AmEx likes when you carry a balance and pay late on the credit cards, as they make more money off of you.
If you need the points before the close of the next statement, you can call AmEx and ask them to post the points sooner, but you also must make a transfer to another program at the same time. I have done this on more than one occasion.
John
This sounds like the points advance feature where you can borrow points against future earnings.