The RCI soda package doesn't have a separate card. They put a sticker on your Sea Pass indicating you bought the package, so you have to show your card each time. In other words, yes, you both have to buy one.
You also get a souvenir cup but you don't have to use the cup. Many people think you can only get soda by using the souvenir cup but they are wrong. If you don't use the cup they give you a standard bar glass of soda per serving.