We've had Disney Visa from day one and have racked up a lot of reward dollars - and have been able to use them to pay for character meals while at WDW, merchandise, etc. You call and get a rewards card (just like a credit or debit card) and then when you are ready to spend the rewards dollars, you can call and transfer the dollar amount to your reward card. Then just present the reward card when you want to use it and they will run it just like a debit card (this is what we did at WDW with it).
As TAKitty said, you'll see the rewards dollar amount on your monthly statement - the dollar amounts stays "on account" until you transfer it over (either by phone or online). For current Disney Visa holders, they had a special character meet and greet at Innoventions West running through 9/30 that includes a complimentary 5x7 photo.