In NYC part of the condition of getting a reduced charge [the misdemeanor charges were dismissed in exchange for your DC plea] is that you receive a conditional discharge along with any other punishment you may receive fines, community service, classes, etc.
The conditional discharge essentially states that you muct complete whatever punishment you were given, pay the court fees, and stay out of trouble for one year - dont get rearrested. If you do not fulfill these conditions, you can go to jail up to a maximum of 15 days.
Remember the record that you're concerned about is not a "criminal" record as you have no criminal conviction since a DC is a violation and not a crime.
This response is for general information purposes only and does not constitute the formation of an attorney-client relationship. Past results do not guarantee future results.