Here's some references:
https://www.tax.ny.gov/pdf/memos/income/m09_15i.pdf
https://www.tax.ny.gov/pit/file/nonresident-faqs.htm#nyc
My interpretation of all that gobbledygook, is that only undergrads are eligible for the student exception to the residency rules. You are, most likely, a NYC (and NYS) resident for income tax purposes.
