I work in NY and just moved to NJ, should I have my W4 changed to withhold NJ State Tax or is that something that should've happened automatically from my employer?

Don't take a chance . Contact your payroll dept. you have to make sure they are witholding enough to satisfy the RobinHoods in both states.

I know... I work in Jersey and live in NY . NJ and Pa . Have a reciprocal income tax agreement (no commuter tax) but NY thinks it's a unique privilege to live here and does not have such an agreement. What will happen is that NY will collect the difference between your Jersey tax and what you would've paid had you been a NY resident .

During the period you live in NJ, you will report your NY income on the NJ tax return. You will also claim credit for taxes paid to NY. So you will not have any NJ tax or very little tax.

I agree with MukatA.

There is little risk in withholding ZERO NJ tax, because the offset from the NJ credit for NY taxes paid will probably completely offset any NJ state income taxes owed.