Public urination first time offense in Virginia already accepted offer

During mid-September, I met with recruiter of small PE fund in NC during career fair.

Two days later, I get a public urination charge in VA where I go to school (lowest level misdemeanor equivalent to being drunk in public, NOT on sex offender registry - just a bad Friday night)

1 month later = super-day + offer + acceptance

Fast forward to today, lawyer tells me I have to pay 25$ fine and he wasn't able to get this dismissed.

My offer letter which I already signed says that background check is company policy (could be just steam), and also in a separate bullet point that by accepting, I confirm that "i am not bound by anything that prevents me from accepting this position."

They have yet to send me the official background check, or even ask "have you been convicted of a crime?"

Side note - totally clean record otherwise.

Should I be proactive and tell my employer now, or wait until I get asked if I have a criminal conviction, granted they even ask me at all?

*gave off somewhat fratty vibe - told me to make sure I enjoy my last year in college.