“Why do you vomit after anesthesia?”

Anesthetic gases and opioids both trigger neural receptors that can cause vomiting.

Nausea and vomiting are relatively common side effects of inhalational anesthetics and opioids that act on specific brain receptors. Some risk factors predispose to nausea, such as female sex, outpatient surgery, obesity and diabetes, as well as not having an empty stomach or undergoing emergency surgery. Much research has been done on the prevention of nausea and emesis after anesthesia with current recommendations involving the administration of multiple antiemetic agents.

Multiple factors are in play. Vomiting center is stimulated by anesthetic gases, changes in CO2 levels, some anesthetic gases do enter the stomach and the rest of the gut, as the lungs exhale the anesthetic gases out afterwards, some sensitive people may get nausea just from its smell.