It doesn't end up in the “Führungszeugnis” if it's no more than 90 “Tagessätze”, and the first offense. There's not enough information in Jan's toot, but many “Strafbefehle” are exactly those 90 Tagessätze, for exactly that reason that it's then not going into the Führungszeugnis.
Going to court adds another risk: the judge is free to impose a higher fine.