We were there in May and I'm fairly certain they have a shuttle to Disney. However, it's my opinion that you really need a rental car when you are staying at the Vistana. Everything is close but not close enough without a car.
Depending on which section you are staying in, you could have a 10-15 minute walk just to the lobby to catch the shuttle. I believe you have to pay for it as well.
Call the Vistana and ask for specifics (how often shuttles run etc). Then you'll know ahead of time.