TL;DR: She will need to file State forms both with NY and MA.
this job required her to have a New York based address - this means that NYS expects her to pay taxes on the earnings. New York is notorious in treating earnings as NY sourced unless the remote work is for the convenience of the employer. See here:
New York is one of several states that imposes what is called the "convenience of the employer" test in determining if an employee working from a home office outside of the state is liable for nonresident income tax. Under this test, nonresident income tax applies if the employee is working outside of the state for the employee's own convenience rather than the necessity of the employer and the employee spends at least one day in New York in the calendar year. Conversely, if the telework is out of the necessity of the employer, nonresident income tax does not apply.
The employer explicitly demands her not to be out of NY, so her telecommuting is for her own convenience, not the convenience of the employer. So her income from the NY employer will be taxed by NYS as non-resident income sourced in NY, unless she never steps foot in NY.
MA will tax her worldwide income as a MA resident.
There may be a credit given by one for the taxes paid to the other, not sure - check the form.