The general rule is that states with an income tax can tax non-residents on income earned from work physically performed within their borders. (There are some exceptions for those who work in the transportation industry, such as airlines, railroads, OTR trucking.)
Each state with an income tax has a "filing threshold" for non-residents. The details are available on each state's tax website. The filing threshold is the income amount above which you're required to file an income tax return.
Assuming you're a W-2 employee, the only state you don't have to worry about is Pennsylvania. NJ and PA have tax reciprocity for W-2 salary or wages. That means that NJ residents are not liable for PA income tax on their W-2 income.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
