We currently have 2 Disney VISA accounts; each was opened with an incentive offer. After meeting the requirement for the incentive (spend $X within Y weeks) and being billed for it, our incentive was sent. It was a regular Disney gift card. SO
Opened the account and requested a payment due date of the 15th of the month. I got the card, charged the required amount; billing statement was received around the 22nd of the month and the gift card came at about the same time (in a separate, plain envelope). I paid off the bill at the end of the month, when I pay ALL my bills.
Your rewards card is different. For your first card, you need to contact Chase (you can do it online) and request a rewards card be sent, and you need to put at least $10 worth of rewards money on it. I think it takes about 7-10 days to get this card. You can load more rewards dollars on to it at at any time, but the card will expire in December of the year after you request it (so if you request a card today, it'll expire 12/15). ANy rewards on the card expire when the card does, so don't put on more than you think you'll use.
Fortunately, it's easy to add rewards to the card; just go online and request it and, voila! Rewards are on the card. Also, if you have already had one card, you can request a card AT Disney World. Sometimes I do this if it's a last-minute trip, and I'm not sure if the card sent by Chase will arrive in time. (note: I don't' know if they have changed this
it used to be a requirement that your very first card could only come directly from Chase. I've had my VISA card since Day 1.)