Dear Customer -
I don't think you will be paying twice during the year. Your new employer will withhold NJ taxes not NY. When you file your returns next April all of your income will be included on your NY return. Your NJ return will only tax you on your NJ income. The NJ withholding from your wages should approximate your NJ tax. On your NY return you will receive a credit for the NJ tax liability.
Hope this helps.
If you have historically received refunds on your NY return, I would not withhold NY tax from your NJ income. That way your take home pay should be similar to what it would have been if your worked in NY.
As a resident of NY all of your income is taxable there. Because you are also taxed on a portion of that income in NJ, NY allows a credit against your NY tax liability for the NJ taxes.
I should essentially wash out when you file your returns next year.
Were you working in NYC before.
Because you have mentioned that historically your NY tax was higher than what you expect from NJ, you may want to consider having your employer withhold the difference. You should be able to have them withhold a fixed $ amount. As another option, you could make quarterly estimated tax payments to NYS to cover the spread.
I think that rather than paying the difference next April, you should cover the bulk of the difference by withholding or estimated tax payments. That way you avoid the potential of and underpayment penalty.