We were at BLT in May. The only refill station at BLT was out by the pool. It is a small station with soft drinks only. You might can ask for other items at the bar, but I'm not sure. BTW, this station didn't open until the pool bar opened, which was 10 or 11 am, which was a total pain.
Contempo Cafe in the Contemporary has a large refill area, where all beverages are available.
They will refill your mug at the pool at the Contemporary, but there was no self-serve refill station.
Again, this was in 5/12, so 5 months ago.