This issue only seems to occur when the Advanced Forms are enabled.
(Simple forms work fine)
To replicate the error:
1. Enable advanced forms (as described above)
2. Start a submission
3. On the "Access" page, add an embargo with a "Administrator" group (set whatever date you want)
4. Complete the submission. The item will be publicly available immediately.
The problem seems to be that the final archived Item has multiple resource policies attached:
(a) The correct embargo resource policy, based on the embargo you defined (e.g. "Administrator" with a specified start date)
(b) The inherited "Anonymous" READ policy (from the collection). This second policy causes the item to be immediately publicly available despite the embargo policy.
I've been able to replicate this problem both on demo.dspace.org XMLUI (which has Advanced forms) and other 3.2 instances. When the "Simple Forms" are used, this issue does not appear and the Item ends up with just a single resource policy (the correct embargo one).