I think it's a bit more complicated than you're implying here.

Yes - you are technically correct that each country is taxing its own citizens/businesses with tariffs. I also agree that phrasing is more honest than what the article states

But for interconnected supply chains, the result can get pretty muddled.

Ex -

Canada sells wood to a US company. US applies tariff.

That US company sells a component made of that wood back to a Canadian company. Canada applies tariff.

That Canadian company uses that component to produce a good that's sold to US consumers. US applies tariff.

etc...

For the end purchasers of the finished product - the net increase in price (the final "tax" you pay) might be a summation of various tariffs applied by both countries as they interact with each other.

The price increases at the final sale are additive, regardless of which country is capturing the tariff as tax. The real result is that the product is just more expensive to make when tariffs are in place, and so must be sold at a higher price based on the total tax applied to all parts of the product (regardless of where in the chain it was US/Canada/China/Other/Etc actually capturing a tariff).

Ex - you will pay more because of US tariffs, and more again because of Canadian tariffs in response to US tariffs.