Hi,
I have looked into this as I could face a similar situation in the near future.
As per my research, the nominated candidate needs to (i) have the skills, education and work experience to
contribute to the economy of a specific province or territory, (ii) want to live in that province, and (iii) want to become permanent residents of Canada. You can find the information here -
https://www.canada.ca/en/immigration-refugees-citizenship/services/immigrate-canada/provincial-nominees/works.html
There's no rule book that mentions you cannot work from home for an employer in another province, but by doing so we wouldn't contribute to the economy of the nominating province.
That's my interpretation. Do let me know if you think otherwise. Thanks!
P.S. I've decided to work for an employer with Legal status in the nominating province.