There is a myth that cats can drink milk without any problems and that is wrong. The only living being who drinks milk after adulthood is the human being. In cats, as well as in dogs, milk ferments when it reaches the stomach and leads to an onset of gastritis, which can cause vomiting and diarrhea as well.
Feeding cats is very specific and attention should be paid, as incorrect feeding can lead to serious consequences. Whenever implementing a different type of feeding for your cat, consult a veterinarian.