Active duty military getting exemption for New York state taxes

It depends.  New York has tricky rules when it comes to military.  See this website that gives the overview:  http://www.military.com/money/personal-finance/taxes/state-tax-information.html#NY.  

Basically, if you own a home or rent an apartment off post, he is not taxed by New York on his military pay and there is no filing requirement.  If you are on post, his military pay could be taxable.  Two things you'll need to do.  First, make sure his W-2 is marked as Active Duty in TurboTax (screenshot at end).  Second, scroll carefully through the New York return, and there should be an option for amount of military income earned stationed and domiciled outside of New York.  Filling in that information correctly exempts his income if he qualifies.

Your situation may be different:  See this FAQ on Military Spouse rules (especially the Joe and Mary example):  https://ttlc.intuit.com/replies/3302300

If you are a California resident, because you never established residency in New York, then you do not need to file a New York return.  You can scroll carefully through the return and find the Allocation Screen.  It will ask how much of your income was earned in New York, and the answer is zero.  Your income will be taken off.  If both of these are done this way, and the New York tax is at zero (which it should be), you will not have to file the New York return.