I'm applying from FL, the jobs are in CA, AZ, NC, etc.. In state of FL, I understand that Adjudication Withheld means "NO formal conviction", but not sure if this applies for job applications outside of FL.
I read your question as "Must I disclose my conviction on the application?"
Unfortunately, the answer varies from jurisdiction to jurisdiction. If the adjudication was withheld, that should mean no judgment of guilt, especially if you have completed your term of probation etc. However, some states count this kind of disposition (know generally as "deferred adjudication") as a conviction for employment purposes.
Do you know whether your conviction has been expunged? That may be an option as well - an expungement in Florida may mean that you don't have to disclose in another state.
I have a few self-help links on my website that may assist you.
Answers are for informational purposes and do not constitute legal advice for your specific situation.