As far as I know trademarks work per country and per business type. If you register the name “nirvana” for your restaurant in Canada someone can still open a repair shop called “nirvana” because it’s a different type of business. Someone could also open a restaurant with the same name in Argentina, because your trademark is only for Canada. Things of course get more complicated for digital businesses.
Also, when you trademark a brand, at least when I’ve done so, you never trademark it for just one country, there are “packages” already made, so for a fixed price you can get your trademark in all the UE countries for example. Being Canada and the US neighbors I would assume if they have the trademark for the US they will also have it for Canada and Mexico at least, because those are the neighbor countries and because there is probably a “north America” pack.
Like @mrsmith said, it is unlikely they will actually take legal action against you, that’s expensive and usually not worth it. Just consider how would you feel if you were on the other side of the equation. If you had the trademark for the brand and they were using it in the US, would that bother you?
In any case, I’m not a lawyer, I’m just talking from my experience having had to trademark a few brands over the years.