A few years ago, one of our cats, Holly started throwing up after eating her tinned cat food. We purchased our cat food from various places such as Pets at Home, Asda and Sainsburys and it was mostly home-brand food.
The thing is, she had this sort of food for over 5 years and never had such issues before. We sent her to the vets many times, but they couldn't find a cause for her vomiting. After many visits to the vets, and tireless days/nights, the vets finally found that she was allergic to something in the cat food.
We purchased some hypoallergenic dry cat food and higher quality wet cat food and she became happy and well again. We now no longer purchase cheap cat food and all our cats are very happy with their new way of life.
Our higher quality wet cat food contains fewer proteins than most other brands and therefore causes fewer issues for Holly. Holly has always been a bright cat and it became very alarming when she suddenly fell ill.
If you have cats that are vomiting after eating, then I would highly recommend you try to change their food to something of higher quality. It may cost a tad more, but your cat will become a lot happier.
We also learnt that allergies don't always happen from birth, they can build up an intolerance after time and issues may not be as obvious as you would like it to be.