The law will go into effect at a particular time. I'm not sure when NY state applies the new laws signed into law in the current legislative session but it won't be immediately. You'll need to find out when the laws from this session take effect. It may be Oct 1 of this year, maybe January 1st of next year, etc. It depends on how this is performed in NY state.
And those of you who indicated that out of state sales of ammo will increase dramatically are correct. Unless the legislature passes a "non-importation" of ammo statute. Only FFEs will be legally permitted to import ammo into the state under such a statute. Not sure how they would enforce this, but watch out for it. Black market for ammo anyone?