I redeemed EE bonds in 2016, and reported the interest on my 2016 Federal return. Looks like that income also flowed to my NYS return. Isn't that wrong? How do I avoid?

When  you entered the 1099-INT in Federal taxes, Wages and Income; there was a question box where you were supposed to check that the interest was not taxable for State purposes. You may have to now amend 2016 NYS.

Though  #1...ee bond interest should be reported in box 3 of the 1099-INT...and then it should be automatically excluded in the state tax return....if the software is working right.

Though...#2... many states use the full Federal AGI (including box 3 $$) as the starting point, and then subtract the box 3 $$ on a later line....so some people miss that and are mistaken about it not being excluded in the state return.  (Not sure what NY does)

Though #3.... this assumes that the user did not create their own 1099-INT and put it in box 1.  
Those using Treasury-Direct accounts don't get a 1099-INT in the mail...they have to download it from their online Treas-Direct account.  Those who redeem paper EE-Bonds at the bank do get a paper 1099-INT (I think).