TD does not authorize employment, and work performed on U.S. soil for a Canadian employer is still work in the United States. He needs his own category if he intends to keep the job.
Locate the work where it will be performed, not where the payroll sits
TD covers the spouse and unmarried children under twenty-one of a TN professional. It allows study and residence, but it carries no work authorization, and the source of the pay does not change that analysis. A spouse who logs on each day from a U.S.
address to do his Quebec job is performing work in the United States without authorization, and that risk attaches to him and can complicate the household's future entries. If his occupation is on the TN list and his employer can arrange a genuine U.S. role, he can apply for TN in his own right.
If not, the honest options are to keep his work in Canada and commute or visit, or to accept that the U.S. period is one without employment for him. Decide this before the family sells or leases the house.