AZ resident paying non-resident taxes to California on income earned in CA, is AZ inc tax "paid" the tax liability before or after credits for donations to schools, etc?

It is the tax after all credits are calculated (net tax).  It seem you are claiming the "reverse credit" on the California return:  since you are an Arizona resident, you pay taxes on your CA income first in Arizona, and California gives you a credit for the tax you pay on the income to Arizona.  If California's tax is higher than AZ's tax, you will pay the difference on the CA return.  

For that figure, you will use the net tax.  If all of your income is in California, you can also determine this by the net difference between your AZ tax withheld and the AZ refund or added to the additional tax paid.