My understanding from a pamphlet I got a few years ago is that Jette put that comment in anytime sometime travelled out of Quebec (which is where he focused his research). So this would have included anyone who went exploring in the Great Lakes region, trapping in Ontario, travelling down the Mississippi or working in a lumber camp anywhere from Vermont to Ohio.
To figure out why an individual would have travelled outside of Quebec for a time, you'd need to look at the social, political and economic situation in Quebec. Early 1700s saw the French and the Indians fighting the British and each other sporadically all over North America. Anyone in the military would have been moved around. During that same period, the British were causing problems in Acadia and parts of Quebec (the Brits were not friendly at all to the French). Exploration of the Great Lakes and Mississippi river areas were heavy (which explains all of the French names in Michigan, Illinois, Missouri, Mississippi, etc). There were many French settlements in Illinois alone during that time, and many of the Tessiers were living here.
In the early to mid-1800s, the economy in Canada was a disaster. The land wasn't supporting the French, who were loath to co-mingle with the English-speaking settlers. So they started moving into remote regions of Ontario, Vermont, New York, Michigan and Minnesota to set up lumber camps. They'd go back occasionally, especially to have babies baptized back home when they were old enough to travel (especially from the Vermont camps which weren't far from Montreal). Part of the reason that it comes up in Jette is that in the remote areas there weren't any priests on a regular basis. So if they missed the priest in his annual trek, then they'd go back home if there was an opportunity to make sure the babies were christened.
Hope it helps. Sounds like you're having a lot of fun since your link to the family blew open!