I just recently added Issue security to a project, with Public (any log in user can see) and Private (only reporter,assignee, and project role admin).
I am an admin I can see all tickets. When I set a ticket to either Private or Public, it disapears for the JQL (eg key = key-123). I can go directly to key-123, I can see it, I can edit the fields, I can change the security level. It will not show up in the JQL.
If I remove the security level to none, the ticket shows up in the JQL.
The other odd behavior is, if I search the key, then go edit a field on the ticket, the ticket will magically appear in the search without me pressing anything. If I hit the refresh/search button after it has shown up, the issue disappears again, only shows up if I search for it, edit the issue and wait for the ticket to appear in the search.