AZ gives the credit on the non resident return for taxes paid to CA. (AZ and CA are one of those exceptions, generally the resident state gives credit for taxes paid in the non resident state, but AZ and CA are vice versa).  

Im not sure what you mean by the IRS giving credit for taxes paid to another state on the 1040...there is no "other state" on a 1040.  You can use taxes paid to any state as a deduction on the 1040 Sch A, but there is no "other state credit" on a 1040.

"I tried to fill the 309 form and it gives the Credit to a certain extent."

Right it will only give credit for the amount of double tax that was generated, it may not wipe the tax due to AZ out completely.