The mugs are a bit trickier to refill at the Boardwalk than at the resorts with the self serve food court type places.
You have to either fill them at the Boardwalk Bakery, where you show your mug and they give you a paper cup filled with your beverage (they can't refill into your mug). Or I believe you can also refill at the lounge. My hubby did that once last time.