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The credit doesn't apply to ticket purchases, it is intended for seat upgrades, inflight purchases, bagage fees, etc. However, many people have found that you can purchase either gift cards or contribute to your travel fund/gift registry and be reimbursed as well. There are several threads over at FlyerTalk about this practice and depending on what airline you use you may see different results. I know several people who have had good luck with United and AA.
When I've used it in the past it usually shows up as a statement credit within 5-7 days of my transaction. It's always been automatic.
Drew, glad I could help! Don't kick yourself too hard. Put some spend on those cards and PIF, you might get sent the offer for 100k signup bonus. I wish I would have held out but I wanted the card for the benefits and "settled" for 50k sign up, then I recieved a prequalified offer with 100k sign up bonus for one of my businesses. Needless to say, I went ahead and signed up, but will most likely PC the business card in January 2016 before the annual fee kicks in.
Today I got an email with the PRG offer that the OP got. I would go for the Platinum, not sure about the PRG. I wonder if the OP's DW's offer was email or something else.