Typically, your resident state requires you to report your world-wide income on your tax return - no matter where it was earned.
New Jersey will consider you a full year resident if New Jersey was your domicile (permanent legal residence) for the entire year OR, if New Jersey was not your domicile, but you maintained a permanent home in New Jersey for the entire year and you spent more than 183 days in New Jersey. See more here: NJ Who Must File
But, New Jersey will give credit for taxes paid to another state or jurisdiction (NYC) when you complete your NJ tax return and this will reduce the income tax amounts due for NJ. In TurboTax, you will want to complete your returns for your non-resident states first so the taxes paid to other states and jurisdictions will be credited on the NJ resident return.
For New York state, you are only allowed a Real Property Tax credit (on your NY state return) if you were a resident of NY for the entire year. (See more information here: NY Real Property Tax Credit.) New York will consider you a resident even if "your domicile is not New York State but you maintain a permanent place of abode in New York State for more than 11 months of the year and spend 184 days or more in New York State during the tax year. Note: Any part of a day is a day for this purpose." (From NY Income Tax Definitions - use that link to see more information.)
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