How long does it take a theft conviction to show up on your background check?

I have an active warrant (3 months now) for unpaid speeding ticket and a B theft conviction from January of this year. My DARS (govt agency that helps place people with disabilites in jobs) caseworker has run a background check on me and is saying that nothing is showing up on it. How much longer do I have before it starts showing up?
 
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