You get the additional 15k after you spend $5,000. Trust me I just got it my second month. You get it.
You most likely are not seeing it since you are logged in. Apply for the card on SPG.com instead.
What should have happened is that they gave you a SPG number that you should be able to see when logging in to your AMEX account. Then goto SPG.com and "Register" for an SPG account and plug your number in as well as making a UID and PWD. Then your points will be seen in your SPG.com account.
All points will be updated there including the monthly points that you get for spending on the card. Those will update in to your account monthly.
BTW there is something called SPG Moments. There are MANY great events, shows and attractions that you can buy with SPG points. They had two Cirque De Solei tickets out there for 25,000 points. I should have bought them. Hottest show in town for 100% free.