Raise it before you accept anything, and certainly before you give notice at a Canadian job. Whether the company can employ you rather than contract with you is a budget and hiring decision on their side, and it can take weeks to resolve internally.
Settle the structure before the resignation, not after
A restructure from contractor to employee usually needs a hiring manager, a finance approval and sometimes a payroll registration in a state where the company may not already run payroll. None of that moves quickly, and none of it is under your control. The sequence that causes real harm is the one where a Canadian position has already been resigned, a start date is fixed, and the immigration question is asked in the final week. Set your own checkpoint: no notice given until the American company has confirmed in writing that it will engage you as its employee and has issued a letter describing the professional duties. If that confirmation does not arrive, you still have a job in Innisfil and a decision to make with better information than you had before.
Hypothetical example: Sofia, a speech-language pathologist, is asked to start before the employer has approved an employee role. The first milestone is a signed employer arrangement that rules out self-employment and accurately states the professional duties. Citizenship, the listed TN profession and its credential or licensing rule should then be checked before travel is booked. A Canadian citizen may request classification at a port of entry, while the employer may instead file Form I-129; neither path authorizes work before status is granted. Sofia should set a document-completion checkpoint ahead of the proposed start so business urgency does not turn an unresolved contractor arrangement into an incomplete application.