Tax must be paid for rentals less than six months.
From a floridarevenue site:

What is Exempt?
Rental charges or room rates paid by a person who entered into a bona fide written lease for continuous residence for a period longer than six months are exempt.

I don't know what the rules might be for including tax in the listed rental price.

If it is a 6 month or less rental, tax is due and must be paid by the landlord to the state. If it is not paid, the state will come after him. If he is not charging you the tax explicitly, then he is probably just burying in the rate he is charging you. Charge you 10% more and pay the state 7%.