I have deployed a Enterprise Geodatabase in a PostgreSQL server and would like to request support in two questions:
1. Out of the box, Editor Tracking..but this will not track deletes
2. How To: Enable editor tracking to record time in database time
Enable Editor Tracking—Help | ArcGIS Desktop
You can record the dates of edits in either the database's time zone or in UTC (Coordinated Universal Time).
What version type you are following:
1. Transaction versioning
2. Branch versioning ( This is based on time stamp)
Regarding timezone, you can capture data and time in PorstgreSQL itself without ArcGIS and check what timezone it is capturing. That will help to narrow down the Timezone issue.