What does "in control" mean in this case? How do you "control" a city?

Being there with the military and not having an opposing force is one thing, they could do that. What benefit would they get out of such occupation though?

There's usually one of 2 purposes to an invasion, capture the territory and make it part of your own for financial purposes, or to kill everyone (or a large portion) to free up space for your own people to take over.

However, getting anything financial out of invading Canada is impossible realistically. They can't just come in and directly capture the tax dollars or something, none of that even exists physically at this point for a start, and any sort of force they use is just going to result in people refusing to pay taxes, the economy tanking, and them not getting anything anyways. They would have no way to enforce anything against such mass resistance.

They already get most of the resources we produce, the Oil in Alberta almost entirely flows to them for example. If they invaded they can say goodbye to that, even the US military couldn't protect that much pipeline from terrorism.

There's just no useful goal to invading Canada in the first place, so if they do it out of pure spite they're going to have to contend with their own population being absolutely livid about it. Like full riots in every US city livid. It will make the Palestine and BLM protests look like an episode of Mr. Dressup.