DUI deferred

The key portion of the question you are answering is "or had a prosecution or sentence deferred or suspended"? What you entered with your DUI was a deferred prosecution under RCW 10.05. So the answer is yes.

I wouldn't feel comfortable just telling you to anser "yes" without knowing more. It's easy to say that since the application asks, "Have you ever had a prosecution deferred?" that entry in a deferred prosecution would require an answer in the affirmative. I don't know if that is that simple. There are different ways that a prosecution could be deferred. A "deferred prosecution" is a stautorily created construct, one of the purposes of which is to allow someone who has a problem with alcohol to avoid prosecution by completing a rigorous alcohol treatment program. During the period of deferment the case is placed in a special file and not viewable to the public. There is a veil of anonymity that covers a deferred prosecution and there is a public policy argument that seems to support the idea that a person need not have to give up that privacy.

With all of that said, your question is probably best posed to an employment lawyer who will best know what is expected from you in that arena of law.