The way this worked on our May 22 sailing was as follows:
You can get the drink of the day at the "special" price if you first pay a little more to buy one in a souvenir cup. Rather than have to carry the cup around all week, they put a sticker on your S&S card. You flash the card, they see you've bought the souvenir cup, and you get the Drink of the Day at the special price (in a regular non-souvenir cup).