Minor traffic infractions generally aren't "criminal" and therefore don't have to be disclosed. Speeding 12 over certainly isn't criminal and failure to control vehicle doesn't sound criminal. Speeding 30+ over, reckless driving, DUI, etc are generally criminal.
Most States require at least some court appearance for a criminal conviction, but that isn't a hard and fast rule.
Are very minor damage (e.g. lightly scraped bumper type) hit-and-runs with a parked vehicle (as that accounts for the overwhelming majority of hit-and-runs according to insurance companies) -- that involve a court appearance -- considered "criminal" by DHS when the police never made an arrest but identified suspects with the charges pursued in courts by prosecutors where the cases end up as a civil compromise of sort?
Street parking in NYC or Chicago comes with a lot of these kind of minor fender-benders.