If I'm reading this correctly, the OP was watching the light for cross traffic, and started his motion when the light for cross traffic was yellow, or as I've always called it, "jumping the light."
Sounds to me like another victim of Tolerance Zero or Zero Whatsits or whatever the hell NYC is calling it's policy of punishing cyclists and pedestrians for getting run over in ever greater numbers.
That said, any video of the intersection crossing in question? Without that, it's your word against the traffic cop, and NYC strikes me as one of those places that pays the officers to go to court days.
Here in California, most jurisdictions don't give a crap about cyclists at all. I've jumped lights directly in front of a police car, they don't even take notice.
The extent of my police interaction has been a cop (who currently had a homeless guy off of his bike) pointing and giving me a thumbs up for wearing a helmet.
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