Data Point:
About 1.5 weeks after requesting the extra 15k miles by SM, I got an email that said:
Hi, VegasGambler. We've added 15,000 Citi® / AAdvantage® Platinum Select® World Elite™ Mastercard® miles to your Citi® / AAdvantage® Platinum Select® World Elite™ Mastercard® account. You'll see this mileage adjustment on your statement within two billing periods.
I've met the minimum spend on the card, but not yet had a billing statement since I met the spend (there was one billing statement just after I got the card, before I spent anything)