As far as I know, the only state that taxes non-resident independent contractors is California. CA taxes non-resident independent contractors on services provided to CA-based clients, even if the work is not performed in California.
With regard to other states, the general rule is that you are taxed based on the location where you actually (physically) perform the work, regardless of the payor's location.
I think the correct answer to your original question is that the income you earned from work you did in Alabama would be subject to taxation by Alabama, not by New York. New York does not tax non-residents who never physically work in New York.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
