State tax filing

This Pennsylvania Department of Revenue website addresses Pennsylvania's ruling on telecommuting.  It states:

If your employment agreement provides the employee with a physical workspace at the employer’s Pennsylvania location and the employee elects to perform their work outside of Pennsylvania, then the income for that employee is allocated to Pennsylvania.

I do not know whether you have an employment agreement or what the employment agreement says, but it sounds like Pennsylvania state income tax has been withheld on your W-2.

If 

• Your employment agreement allows you to work in Tennessee and not pay Pennsylvania state income tax, and
• You are a full-year resident of Tennessee, and 
• You file a nonresident Pennsylvania state income tax return, and 
• You claim no income earned in Pennsylvania on your nonresident Pennsylvania state income tax return, 

You may receive a refund of Pennsylvania state income taxes for the time that you worked in Tennessee.

As an example, you worked 52 weeks x 5 days per week = 260 days of employment.  

If you worked only two weeks in Pennsylvania for training purposes, you would report 10 days / 260 days or 3.85% of your pay as Pennsylvania income.  

Be prepared to justify your Pennsylvania nonresident state income tax return if Revenue questions your tax return.