It depends, and there is no magic formula answer. An increase in assessed value does not necessarily equate to an increase in property taxes. Consequently, your taxes can increase without an increase in assessed valuation.
Taxes are determined by multiplying your assessed valuation times the tax rate. A variance in either factor can change your tax amount. In order for taxes to decrease there must be either a decrease in assessed valuation or a decrease in the tax rate (which can occur due to a tax rate rollback, the statutory protection provided to limit the increase taxing entities can receive from reassessment). Likewise, an increase in either assessed valuation or tax rate can cause an increase in taxes.
The tax system, created by the legislature, is set up to keep the valuation and taxing functions separate. To provide for fair and accurate assessments, periodic updates (reassessment) are required, ensuring fairness and equity in property values. After the values are completed, the political subdivisions set the tax rates, determining the amount of taxes you will pay. The assessor only deals with assessed valuation; the assessor has no control over tax rates.