In AZ, the county will adjust the market assessed value of the property itself first. This applies to the following year. This in itself does not mean anything. Later in the year, the tax "rate" is determined based on the upcoming budget. The county has to pull in the revenue they need to operate. The tax "rate" is determined from this.
Even if the assessed value goes down, the tax rate is likely to go up. There may be little or no reduction in taxes.
Each Arizona county makes their own determination based on their budget.
Arizona Homes and Land