Buying from private party in California

To answer your specific question : In order to get a temporary registration to operate it back home , you will need to call or go to your AZ DMV to explain your plans in CA as a private sale where you are the buyer.
While you are there, ask them about who, where and how you pay the sales tax ! You need to know what paperwork they need from the seller which will probably include AZ DMV forms.

* Unless you already know the vehicle and/or the person in CA from who you are making the purchase, this might not be the best idea.
Out of state private sale is the most risky form of sale. It must be worth it monetarily to buy from an out of state private seller and you need to know its a clean title. Hire a professional rv inspector.

You will need the VIN number from the seller in order for you to insure it.
You have a lot to do involving DMV, your INS co. and a Ca. RV inspector to check it all out for you before you attempt to drive it anywhere !

California is beyond weird when it comes to taxation on vehicles. Not sure how it works for private sales, but if you buy from a California dealer and want to title it out of state the dealer has to have an employee drive the vehicle to a neighboring state before you take possession, otherwise you are on the hook for state sales tax and the dealers aren't going to risk their licenses buy winking and nodding that you took delivery out of state. I have done it twice since California is the best place to get high end sports cars and I have a home in a no sales tax state. One time, the dealer even took a picture of me and their driver swapping keys under the "Welcome to Nevada" sign (I drove a dealer car and their driver drove my car) The savings are came close to 5 figures each time.
If it was me, and the seller either didn't know or didn't care, I would get the title and a bill of sale from them and high tail it out of the People's Republic being careful to not attract undo attention by testing the performance limits of the new RV. Arizona couldn't care less about how you got the vehicle, they just want their ounces of flesh when you get your Arizona registration and plates.

Many states require immediate registration, even to just drive out of the state. Check the DMV in both states, as I'm sure both have rules for your situation to retain their revenue. It can't be the first time they're run into this.

I D go to your dmv office and get the facts even write them down. all stats are different.