Let's say you have created a date custom field in the "Fields" tab of the listing type, and want to display it in the listing page with the correct format.
There are multiple ways to do this depending where you are displaying the date.
Edit listing type > single page > cover details. To the right click the "Event date" preset to add it.
Once it's added, click on it and make sure the correct date field is selected under "Field" dropdown
Also, under "Format" dropdown choose Date
That should be it, the date should appear in the listing page cover details area in the correct format.
Important: This method uses the default wordpress date format that you have chosen in wp-admin > settings > general