A user with administrator rights sees all my event details, and the Calendar is visible under the administrator's My Calendars instead of Other Calendars.
Why is this happening? Administrators have full access to all calendars in a domain, and can see all event details, regardless of whether individual users have shared calendars with them. This is necessary to allow them to troubleshoot issues with their users directly. Super administrators can also create events in all calendars in the domain, based on their permissions as super administrators.
This is expected behavior and can't be changed.
For an overview of Google Calendar sharing settings, please see this article on the different ways you can share your calendar.