The tip portion you're talking about is ONLY for UberTaxi, which is different from UberX, UberXL, UberBlack and UberFamily you use at Disney.
OP, I agree with everyone that I would never travel with that much cash. If you have the money to take with you, why not open a credit card to use strictly for the trip and pay it off immediately upon your return home? You are MUCH more protected that way. Even with a debit card, you will have a hold on the account for resort incidentals, and you run the risk of someone stealing the number and you're left without money to pay while the bank straightens it out.
If something happens with a CC, you are not responsibly for fraudulent charges.
Even having thousands of dollars in gift cards would make me nervous, because if any disappear from your room or your wallet, they're just gone.