I am a full time remote employee in NJ. The company I work for is in PA. I'm not seeing the Turbo Tax is completing a NJ tax form.

Which state is on your W-2?  Did a form for PA generate?  In the beginning interview questions did you tell TurboTax you earned money in another state?  If so, go back and change that, as your income would be considered earned in NJ, not PA.

If you work remotely in NJ for a company in PA, you should only be paying taxes to NJ, not PA.  So, you should only have taxes withheld for NJ.

Even if you cross the border and physically go to the office in PA, your wages would not be taxable to PA as PA and NJ have reciprocity meaning you only pay taxes to the one you live in, even if you work in the other. 

If taxes were withheld for PA and not NJ, then you will need to fill out a PA non-resident return and enter $0 as your wages earned leaving the full amount withheld as the amount withheld so you can get that refunded.

If NJ still doesn't pop up, even if you listed NJ as your address, you can select Add A State when you get to the state section.   You will claim all of your income on your Nj return.