This is mostly correct. Prior to 1999 individuals who worked in NYC were required to pay the ~2% income tax regardless of residency. This included people from NJ and CT. They're no longer subject to the tax (the reverse is untrue; I live in NYC and work in NJ, but I'm still required to pay NYC income tax). Historically this was known as the "commuter tax."

Since 2009 residents of NY who live in counties adjacent to NYC are subject to a 0.34% tax if they work in NYC. I believe this tax does not go toward general NYC operations, but rather helps fund the mass-transit that supports their commute. See: https://en.wikipedia.org/wiki/Commuter_tax