It sounds like, even though you will work in New Jersey most of the time, you will still be doing some work in New York. You have to pay New York tax on the income that you earn for working in New York. Your company should keep track of the days that you work in New York and the days that you work in New Jersey. They should withhold tax for each state based on the amount of time that you work in that state, and your W-2 should show New Jersey wages based on the amount of time that you worked in New Jersey. You will still have to file a New York nonresident tax return for the income that you earn in New York, in addition to your New Jersey resident tax return.
New York has an unusual rule that the New York wages in box 16 of your W-2 has to be the same as the federal wages in box 1. So on the W-2 it looks like all your income is from New York. You adjust your New York income on your New York tax return, based on the number of days you worked in New York. You probably haven't paid any attention to that adjustment in the past, because all of your income was from New York.
You will get a credit on your New Jersey tax return for part or all of the tax that you pay to New York, as you have in the past. The credit will, of course, be smaller because only a small part of your income will be from New York, so you will be paying much less New York tax.
I suggest that you keep track yourself of the number of days you work in each state, to make sure the company is getting it right.
