Read the statute.
There is nothing in there that provides any kind of tax exemption.
As far as I know there are no "transfer taxes" in Arizona. And I've lived in AZ for 43 years and have bought and sold many homes.
What taxes do YOU think this exempts you from? Be specific. Name the tax.
You pay a fee of $2 per deed if you have to fill out the affidavit form in addition to any recording feed charged by the County Recorder.
Since you appear to be exempt from the affidavit you don't pay the $2 per deed but you do pay the recording fee which is $15 for each deed that you record:
The schedule is likely the same in other counties or close to those fees depending on where the property is located. You can get your fee schedule from the County Recorder where the property is located.
One more thing. There is no reassessment of tax value at time of sale. The reassessment is done annually on all properties in Arizona and assessment notices generally go out in February (at least they do in Maricopa County).