Were you ordered to do the class by the court? If so, then yes you got diversion. If you never went to court or did not do anything at the behest of the court OR the district attorney's office, then no case was ever filed against you. I have seen this scheme lately - the store and store security get you to go to a class and pay a large amount of money in exchange for not calling the police. It's a scam - unless you are ordered to do anything by the court (or told to in exchange for no prosecution by the DA), you are under no obligation to do anything.
Mr. Feasel is a former prosecutor in San Mateo County (CA) with over 10 years of criminal law experience. Nothing stated on this site shall in anyway be construed as legal advice, or as creating any attorney/client relationship. If you would like to hire Mr. Feasel to further investigate your situation, feel free to contact him thru this site.
Mr. Feasal raises some good points and has some good questions. Were you ever arrested by the police and taken to the police station for this petty theft, or just detained in the security office in the store? Did the police take a mug shot and your fingerprints? They would do that for misdemeanor charges. Were you arraigned in a courtroom and pled "not guilty" before you were offered this class to go to. If the answers to all those questions is "no", you won't have anything on your record, including an arrest.
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You need to consult with a licensing attorney. You should also check the application that you are applying...usually there is a definition of the terms that are used. See if they define what they mean by "deferred adjudication".
In California, terms related to a deferred judgment vary from jurisdiction to jurisdiction. Some have names like "plea in abeyance" "deferred entry of judgment" etc. Some courts want you to plead guilty in order to receive the benefit and then they put sentencing off until you completed whatever you needed to do in order to receive the dismissal. While other courts do not require any plea to be entered.
There are various consequences that you have depending on whether you entered a plea, didn't enter a plea, whether the case was filed not filed, etc.
It sounds like you might have a valid concerns and therefore you should consult with the licensing attorney I suggested. You might get a free consultation or in the alternative a small fee that you could pay and you would know the legal answer to your question.
The above information does not establish an attorney client relationship nor is it meant to provide legal advice.