Remote worker in TN but Employer in NY

I work remotely in TN for a company that is based in NY. I did not have any NY taxes withheld on my paychecks. I'm not sure how to handle this. Do I file a nonresident return with NY? I've seen information about the convenience of employer rule, etc., but I am still confused. I did not work a single day in the state of NY. All of my work was completed in TN. I do not have a state income tax in TN.  Do I owe NY state taxes?