For state income tax purposes, the relevant concept in your situation is one of domicile. You can have only domicile at a time. If NJ is still your state of domicile, then all your income is taxable by NJ - regardless of how many or how few months you actually stay in NJ. NJ has a tax publication that explains the concept of domicile in detail. Here's a link to that publication:
https://www.nj.gov/treasury/taxation/pdf/pubs/tgi-ee/git6.pdf
In order to become a tax resident of Florida, you would have to abandon your domicile in NJ and establish a new domicile in Florida.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
