Your W-2 will have two lines of state information in boxes 15, 16, and 17, one line for NY and one line for NJ. If box 16 on the NJ line shows the correct amount of NJ income I would not anticipate any problems. Hopefully your employer has been keeping track of how many days you worked in each state, and will report the income accordingly. (Also hopefully they have been withholding tax for the two states based on the days that you worked in each state.)
Box 16 on the NY line will have your total income, the same as the federal amount in box 1, because New York has an unusual rule that it has to be that way. Any adjustment to New York income is made on the New York tax return. But obviously New York knows that the income shown on the NY line might not all have been earned in New York. That's why the NJ amount in box 16 is important. The higher NJ income on your W-2 will explain the lower NY income.
