New York is one of the few states that DO tax remote workers in certain instances. They have what is known as the Convenience of the Employer Rule. So if your employer requires you to work from home then you then it is not taxable to NY. If it is not for your employers convenience then it IS taxable to you whether or not you physically go to NY or not.
It doesn't really matter whether or not your employer withholds taxes or not, it only matters if it is for your convenience or their convenience. If you were going to the office up until you moved to another state and they allowed you to work remotely, it would be for your convenience and you would need to pay taxes to NY for this income as a non resident.
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