Are they throwing up because they don't like it or is it a texture thing? If it's a texture thing than I'm not sure what you can do for it. To this day there are still foods/textures that will make me gag. It's not pleasant when it happens, especially in restaurants!!

If they are doing it because they don't like it and think this will allow them to not have to finish than I would make sure they know this is unacceptable and when it's all cleaned up they would have to try one more bite. (of fresh food!! lol)