The convenience of the employer rule applies to certain taxpayers who work from home. It means you're taxed as if you work in your employer's state even if you don't, which is the case here. So it is possible that you owe a large amount to NYS because the entire amount of income earned on the job is taxed in NYS.
if you have other income such as dividends, interest or investment income, these need to be excluded from the NYS return. There are allocation screens in your NYTS return to exclude these items from NYS income.
NJ is a state that taxes all income no matter where it is earned. It does give you credit for taxes paid in NYS thus the tax consequence has a lesser impact than in NYS. You make think you are being double-taxed but in reality, you are not because you are receiving a tax credit for the taxes paid in NYS. You did mention you received the tax credit in your NJ return.
You prepared the return correctly. You prepare the NYS non-resident return first to receive the tax credit and then the NJ return.
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