"NY employer, reported my earnings to FL"
FL doesn't have an income tax dept to report to. I wouldn't think that the fact that the employer may have been reporting wages to the FL dept of unemployment, instead of NY UI, doesn't change NY's ability to withhold income tax. As previously explained, in this thread, you are required to pay NY income tax, under the convenience of the employee doctrine and your employer was correct to withhold it.
I'm not sure what your question is. I originally took it to ask "how do I get one of these states to pay me unemployment compensation?"
