Yes, if you are working remotely for your convenience.
No, if the company asks you to work remotely for their convenience.
Employer convenience would be situations were the company needs you in that other state to work on a project located in that other state or if the company has no physical office space for you at their location or REQUIRES you to work remotely.
According to the state of Pennsylvania:
“A non-resident employee who is required to telework full-time from home in another state should treat his compensation as non-Pennsylvania source income even if his employer is located in Pennsylvania.”
So do I need to submit anything to prove this requirement in order to not pay PA tax?
If you believe you qualify to have your wages not be treated as Pennsylvania income, then you don't need to provide anything to Pennsylvania unless your W-2 shows Pennsylvania wages and state tax withholding, in which case you should file a Pennsylvania nonresident tax return.
Contact your employer if you believe you have incorrectly had Pennsylvania withholding deducted.