NY is one of 7 states to apply a tax to telecommuters using a "convenience of the employer" rule. Basically, if you work for a NY business and move to a no-tax state for your own reasons to save taxes, NY still expects you to pay state income tax on income from that NY company. But if you move for the convenience of the company (such as, you are a salesperson and they change your territory) then NY will not tax your income in your new state.
It sounds like you work in Florida for the convenience of your employer, but you may want to seek professional advice if you aren't confident in that answer. Some random people on the internet aren't going to be around if NY audits you.
