The offers are different than the points. The offers are special promotions available if you use your Disney Visa to purchase them.
As for your reward points, you can use them at WDW just like a credit card. You actually get a physical credit card, with a 16 digit number, signature block on the back, magnetic stripe, etc... your points translate directly into dollars. 20 points = $20 to spend at WDW. The only catch is it has to be a Disney-owned vendor. That excludes Rainforest Cafe, most of the Downtown Disney restaurants, any non-Disney owned shops at Downtown Disney, etc. Except for Rainforest Cafe, I don't think there's anyplace within the four theme parks, two water parks, and all Disney-owned hotels that will not accept the Reward card - so long as they normally take credit or debit card payments. Cash-only locations will not take the Rewards card.