Hi Mathew,
what kinds of taxes are calculated depends on a lot of things. A rule of thumb that is correct most of the time is that the tax country being determined depends on the ship-to location.
The tax country in turn will determine the tax report where the invoice will be declared.
So in your example: I assume seller (your company) is located in the US. Customer is located in Canada and that is also the ship-to location. This (most likely) leads to a tax country Canada in sales order/customer invoice.
As soon as tax country Canada is determined jurisdiction codes of any involved parties do not matter anymore as the transaction has been classified as being taxable in Canada. The document will not show up in any tax reports for the US.
Hope this helps!
Best regards,
Stephan