I have been a resident of PA through the whole year of 2018. I worked in NJ from Jan to Oct'18. I have received 2 W-2s from my employer, one listing PA state and one with NJ. I believe NJ and PA have tax reciprocity with regard to W-2 wages.
Do I need to file tax returns for both states ? Or does this change with tax reciprocity in place ?
You're correct, NJ and PA do have tax reciprocity for W-2 wages.
If your only income from NJ was W-2 wages, you do not have to file a NJ tax return. That income is taxable only by your home state of PA. If that's your situation, answer NO in the My Info section to the question about having income from other states.
>>However, if your NJ employer mistakenly withheld NJ state tax, you'd have to file a non-resident NJ return, showing zero NJ income, in order to receive a refund of those taxes.
PA residents who work in NJ should file Form NJ-165 with their employer. Here's a link to that form: https://www.state.nj.us/treasury/taxation/pdf/current/nj165.pdf
I was taxed PA resident tax and NJ state income tax for my W-2 wages. I don't work for that employer anymore. Does that mean I need to file a NJ non-resident return?
You would need to file a non-resident NJ return if you wanted a refund of the incorrectly withheld NJ state taxes.