If you stir in sufficient sugar, to saturate hot coffee, then you must expect to initially add more solid sugar than is needed, or it will not achieve saturation while stirring.
As the coffee then cools, and the Ksp falls, sugar will continuously precipitate out of solution, adding to the initial excess of solid sugar.
I feel sorry for those unfortunate people, who add sugar to make their poor quality coffee drinkable. Visitors to Australia are often surprised by, and comment on, the higher quality of the coffee available. I guess that partially explains why tourists, when they first arrive here, are in the habit of adding sugar to their coffee. It also suggests that Australia competes on taste and smell, while the rest of the world is competing on profit margin. I have never attended a "Star-bucks", but it seems like an excellent name, for selling shares to US investors.