It all comes down to who has pricing power. If Canadian exporters can raise prices without unduly harming sales, then the tariffs on their goods are predominantly paid by American consumers. If the US cannot, then the tariffs on their goods are predominantly paid by American exporters (and must be absorbed by reducing profit margins).

Whether or not that is true, I have no idea. One would expect there to be enough diversity of trade that on the balance it cannot be that lopsided, but maybe that's wrong. It is certainly possible for one side of a trade war to be hurt both coming and going, without any logical inconsistency.