State tax filing

Thank you for your helpful reply to the OP's inquiry. It is closely related to mine, but I fear something remains unclear to me. 

 

In my case I too am working remotely in NJ full time for a NY company, but they have apparently opted to only withhold NY taxes. When selecting withholdings as part of the onboarding process, should I select an amount for both NJ and NY? This seems to me that it would be in fact causing the double taxation that NJ would otherwise credit. Am I supposed to go the tax year opting additional withholdings for two states only to be credited for one when tax season comes around (accepting that NJ will only credit up to my liability for the state)?