My cat vomits undigested food

Many cats do do this, often the answer is they simply eat to much to fast. I see this most often in free fed cats, though alergies are also a likely cause. If your cat is under 1yr old, I would continue with the Kitten Chow since you aren't seeing a problem with it. Also, cats will do this when the diet is changed suddenly, so when changing to an adult formula, begin adding it slowly to the kitten chow, adding a bit more every day until after about 2 weeks you have made a total switch.

You cat is just gulping down the food too fast and too much at a time. I've seen cats do this especially when given people food.

Try limiting the amount per feeding session and make the sessions routine.