Judically dismissed means that a court has entered a judgment dismissing the charges. As it relates to the statute you cited, it requires that the charges be dismissed pursuant to Penal Code (PC) section 1203.4. If you qualify for it, you must petition the court to set aside the conviction and enter an order of dismissal as provided in PC § 1203.4. I'd advise using an attorney for this.
As I recall California has a statute that prohibits misdemeanor convictions from showing up on consumer reports after 7 years. That is not a dismissal or eradication of the conviction.

