Oh, dog food will most definitely cause vomiting. For some reason, cats seem to love it. It's not good for them. Try to keep an eye on him when the dog's food is out.
We always put the dog's food out for no more than 10 min. By that time, the food is gone and the cats have no chance of getting it.
The guess is food allergies, so we are going to try hypo-allergenic food. My daughter said she saw some dog food in the last batch of vomit from the cat, so he must have gotten a hold of some of that. Also, we are going to try to feed him more slowly because he was eating so fast.
Keep in mind that antibiotics can also cause vomiting and diarrhea too. Are the stools just loose or is he going a number of times? If he's going a number of times in a few hrs time, then I'd worry about the possibility of dehydration.
It's a great sign that he's got good energy and a good appetite.
What was the diagnosis? Worms?