1) California company may have nexus in Arizona:
Determining Nexus within Arizona:
The following is a general guideline of activities that, if engaged in, may exceed the minimum threshold of nexus and subject the business to the Transaction Privilege Tax, or Use Tax requirements of Arizona:
Employee present in the state for more than two days per year.
Ownership or lease of real or personal property in Arizona.
Maintenance of an office of place of business in Arizona.
Delivery of merchandise into Arizona on vehicles owned or leased by the taxpayer.
Independent contractors or other non-employee representatives present in Arizona for more than two days per year for the purpose of establishing and maintaining a market for the taxpayer. Examples of establishing and maintaining a market include: soliciting sales; making repairs; collecting delinquent accounts; delivering property sold to customers; installing products; conducting training for employees or representatives of the company or customers; resolving customers complaints; providing consulting services; soliciting, negotiation, or entering into franchising agreements.
2) California company might have decided to voluntarily collect Arizona sales tax.
3) And even if the California company wasn't collecting Arizona sales tax, you would owe Arizona use tax.
Your use of the word "supplier" indicates that this is a business transaction rather than personal consumption. Are the purchases for resale?