A lot of cats vomit after eating, if they eat too much, or have a lot of hairballs, that can cause them to regurgitate their food. Sometimes, they gulp down food very quickly, and then throw up what looks like the food before they ate it. Look for hairballs in the food, and get something like Cat Lax, or Laxatone that is a hairball remedy that you can place a dab on your cat's paw, which they will usually lick off and it will help them pass the hairballs.
Do not give too much food at a time, to your cat. Dry food usually seems to cause the most vomiting in my cats when they hurry and eat it or have hairballs.
As far as your son vomiting, it could just be coincidental, or sometimes, cats can carry certain zoonotic diseases, which can be passed between cats and humans. Perhaps a parasitic infestation could cause vomiting, such as roundworms. Please have your cat's stool checked for worms or parasites. Giardia, toxoplasmosis, and worms, among others, are some of the specific problems that can affect animals, and also be passed to humans.
If your cat does by chance have roundworms, please notify your son's physician and ask him what he thinks you should do. You may need to have your son thoroughly examined and have a stool sample checked out also.
Please see the following website that has a lot of good information on it about zoonotic diseases.
God bless and good luck!