I Just got my first SW card, the miles didn't post for me until I'd paid my first month's bill. I actually did a "one-time payment" because otherwise I would have had to wait another 3 weeks for the auto-withdraw to take the $. Miles were posted a day or two after I initiated the one-time payment.
I wouldn't worry you're the first person they're trying to screw over. They have plenty of money and plenty of miles...