Tax rates are set on the third Monday of August each year. The Board of Supervisors of each county have a budget they have to pay for each year. The tax rates are adjusted each year to pay that budget. So in theory your taxes should be the same each year regardless if your value changes if the budget stays the same and there is no new construction in your taxing district. That is theory though and doesn't occur since budgets change, values change and assessment ratios change for different classes of property.
There are some legislative constraints that prevent certain tax rates from going up very quickly but there are no constraints on the rates being lowered. You will notice that you actually are taxed on two values, not just one. The primary value or limited property value is where the majority of taxes are collected. These taxes pay for schools, fire, etc. The secondary value or full cash value is the one that is based on what the value of your real estate would sell for in an open market. And it is the only value that you appeal. The secondary or full cash value pays for loans, bonds or certain overrides that have been passed by the Board or voter approved. Generally, three quarters of your tax bill will be the limited property value and one quarter should be from your full cash value. That's not always the case especially in Pima County which has some pretty strange valuation processes that are unique to that County. Taxes also vary depending on which school district you live in. Tax rates generally will be higher in districts that have low property value but high school costs and lower in areas that have high property value and low school costs. In other words, poor neighborhoods with lots of kids pay more in tax than rich neighborhoods with no kids. That's not always the case and depends on how much commercial property exists within a district plus other factors.
Arizona property tax is very complex in relation to the rest of the country. It also has some of of the lowest residential property taxes in the country and some of the highest commercial taxes.