There is no material difference with regards to the DUI process in general, or the license suspension in particular, for people with out-of-state driver licenses who are driving here. The long and short of it is that so long as you drive in Arizona you are subject to the Arizona law. You will have to go to court in Arizona.
With regard to the license suspension, your privilege to drive in Arizona will be suspended 15 days after the suspension notice is served if either the refusal suspension or the .08 suspension occurs. Pursuant to the Interstate Driver's License Compact, DUI suspension info is supposed to be shared between states (there are actually a few states that do not participate in this program). Once that information is shared, is up to the state in which you are licensed as to what consequences, if any, it would impose. Generally, there will be some type of reciprocal license consequence. So, the suspect’s license will most likely, though not definitely, be suspended in his home state, as a result of a DUI arrest or conviction in Arizona.