Ohio has a quirky way of calculating tax. Ohio only has one state return, whether you are a resident, part-year resident, or a nonresident. So what Ohio does is calculate how much it taxes all of your income, and then issues a credit against the tax that would have been assessed on income not earned in or taxable to Ohio. Because of this credit, your Florida income is not taxed in Ohio, but is used to calculate how much tax you pay on your Ohio income. Click on this link for an Ohio website that discusses this tax credit: Determine Residency - Ohio Department of Taxation - Ohio.gov
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