PA does not have a tax reciprocity agreement with FL, since FL does not tax personal income. So long as you are a legal residence of PA, if you earn income in any state that PA does not have a reciprocity agreement with, you pay taxes to PA. The only states that have such an agreement with PA are Indiana, Maryland, New Jersey, Ohio, Virginia, and West Virginia. See https://revenue-pa.custhelp.com/app/answers/detail/a_id/268/~/how-does-working-in-a-reciprocal-agree...
The state of PA is right and you owe state taxes on all of your FL earnings.