[FIELD_NAME] and [cb:userdata field="FIELD_NAME" /] substitutions are always raw values. You're needing the formatted value which requires the usage of the [cb:userfield field="FIELD_NAME" /] substitution format. So you should be able to just replace your userdata substitution usage with userfield usage and will display how you're wanting. More details regarding this can be found in our substitution tutorial below.
www.joomlapolis.com/documentation/279-community-builder/tutorials/18353-using-substitutions-throughout-cb
Another neat trick is our nested substitutions. Nested substitutions are supported for date substitutions. So something like the below also works for custom formatting at only that location.
[cb:date format="jS F Y" date="[FIELD_NAME]" /]