When a new note is added, there is a check box at the bottom to make the note restricted or unrestricted . If a note is unrestricted, anyone with permission to view the item will also be able to read all unrestricted notes on that item. The privileges related to notes (such as "View Notes if Owner" or "View Notes if Submitter") refer to restricted notes.
When you add a " new note " from the Detail Controls in Composer, and check Require New Note on the transition, the new note does not appear on the Update transition and a new note is not required. It works correctly in any other transition, just not in the Update transition.