Not necessarily. The paraquaductal grey region is supposed to dampen pain signals, but sometimes in some people is does not do that. A migraine headache, severe shoulder pain, an inner ear balance problem and a bunch of other things can overwhelm that brain area such that the pain resonates in waves of pain signals that wash back and forth through the area like waves of water in a bath tub until the person vomits.
There are other things that can make you vomit though. Trying to swallow a raw egg or drink something that tastes very bad, eating something that produces too much stomach acid..those will all make you vomit as well. They involve your sense of taste, your sense of smell and your stomach's ability to know when its contents are too acidic to process are all different mechanisms that can lead to nausea.
I would bet that the pathways those stigmata take into your brain are all different as well.
I will get back to my dog. It is well known a dog have one of greatest sensors of smell. I take it the sense of smell is a gas chromatograph , were it identifies a variety of compounds and the organism identifies pleasant and unpleasant.
My Puch, liked, ham, cold cuts chicken . hot dogs . ( everything is identified by smell ). come time , hot dog no good any more, the followed by cold cuts, than ham, and ended with ham and then nothing any more . Then if you force ( mildly )he will vomit.
So this becomes a signal some thing in the system is wrong. Since the system is based on circulating fluids, some compound is introduced with time into the system in larger quantity until reaches a threshold.: then some part in the brain will signal the involuntary reflex to initiate the reverse peristaltic action. So the question is what is the growing compound with time and were is it produced.