Does the traditional IRA reduce your AGI dollar for dollar?

Your AGI is not the same as the taxes you owe.

Making a deductible contribution to a Traditional IRA does reduce your Adjusted Gross Income (AGI) dollar for dollar.  That does not reduce your taxes dollar for dollar. 

The AGI is reduced, thus your taxable income is reduced.  This reduces your taxes, but only by the amount of taxes that you would have paid on the amount of money contributed to the IRA.