We were just at BC two weeks ago, and loved this new refill station at Hurricane Hannah's! It was really convenient when we were at the pool or on our way to EPCOT/DHS in the late afternoon. Didn't have to wait in line or ask a CM - just stepped up to refill. Very easy!
As previous posters mentioned, BC Marketplace also has refill stations. While the Marketplace was open from 7am-11pm, we were able to get coffee from the refill stations as early as 6:30am.