It is extremely unlikely that it is related to his
neutering.
Vomiting is not a symptom associated with UTI. That would show as a change in urination (more or less frequent, apparent pain or difficulty urinating, excessive licking of genitals, etc.). It could just be something he got into or that disagreed with him or that he didn't chew well enough. If the vomiting persists, I would check his stool for any changes (color, consistency, frequency, etc.) and contact your vet.