Since 2010, the metropolitan area (the New York counties of it) is adding more residents than the entire state of New York. The New York counties added 447.042 residents, while the entire state only 417.689.
In fact, of 62 counties in New York, only 19 have grown since 2010:
The five counties of NYC + the counties of Albany, Erie, Jefferson, Monroe, Nassau, Onondaga, Ontario, Orange, Rensselaer, Rockland, Saratoga, Suffolk, Tompinks and Westchester.
Of those, Erie, Jefferson, Monroe, Onondaga, Ontario and Suffolk lost population between 2014 and 2015.
The counties in red, gained population between 2010 and 2015, the ones in orange had a net gain, but lost some people between 2014 and 2015. All the others lost population.
Basically the ones with consistent growth are the ones around NYC, Albany and Ithaca.