Do you guys happen to have a credit card associated with your Disney account? I don't. And I wonder if that's the reason I don't see a link for payment. This would be a strange design decision, but it's possible.
I go to the Disney site, click on My Disney Experience, then select "Customized Maps." This brings me to the old site, upon which I click "My Reservations." This displays my hotel and dining reservations, so I click on "View Details" for my hotel.
Tinkerbell appears, then my room reservations appear, with details (Grand Total, Deposit Paid, and Balance Due). Nowhere on this page is a hot link or button or any other text about paying.