From the Arizona Child Support Guidelines: If child support for more than one child was ordered under these guidelines and thereafter the duty to support one of the children stops, the order is not automatically reduced by that child's share. To obtain a modification to the child support order, a request must be made in writing to the court to recalculate the child support obligation pursuant to these guidelines. The procedure specified in Section 24 may be used for this purpose.
Basically, yes you have to inform the court in writing to modify the order.
This post is general information about divorce and family law in Arizona, and is not legal advice. Divorce is a complex process, and taking legal action without the one-on-one professional advice of a lawyer can produce unexpected results.
Do not wait on DES. Arizona does not allow retroactive modifications, so every month you wait to file and serve the other parent with a petition to modify is a month you lose.
Arizona even offers a "simplified procedure" for child support modifications.
To be clear, DES will have to be notified of the Petition, but I absolutely would not wait for them to file, since you never know when or if they even will.
A qualified and experienced family law attorney can of course assist you in getting where you need to be. Most of us offer free, 1/2 hour consultations, in which your matter can be discussed in detail. That would be a great opportunity to discuss any further procedural or substantive matters.