have eaten at 50+ Disney restaurants and would say it totally depends on the server. We have been charged for coffee after having soda with the meal. And other times we have declined the coffee when offered,saying "we already had our dining plan beverage" and the waiter says "oh I can give you coffee with your dessert, not an issue."
Our experience has been they're more apt to charge you for the 2nd beverage (the coffee) at Non-Disney-owned restaurants...places like Les Chefs, Via Napoli, San Angel in Epcot...Yak & Yeti at Animal Kingdom...Maya Grill at Coronado Springs and so on. The Disney-owned places seem much more flexible with the little extras.