You should be fine if it was a simple DUI but if you get anything but an approval not hire an attorney.
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The interviewer may need a supervisor to review the application simply because you have a conviction. While a DUI conviction is not typically a deportable offense, your application could be denied as a matter of discretion because of the DUI.
Right now you should not worry. Be patient for a few weeks.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
If it is a single, straightforward DUI, you should be fine. If your application is not approved or they request additional information, it would be wise to speak with a local immigration attorney with experience with your local USCIS District Office.