Change the permissions to access Volunteer tab in CiviEvent
The two places "Edit All Events" is defined as necessary is in the page callbacks in the router XML on lines 19 and 27.

You should be able to change those, then do a cache clear with menu rebuild to change the permissions.

Since CiviVolunteer is so AJAX-heavy, I'm pretty sure that's the right answer.  You can probably just remove the "Edit All Events" permission.  However, the better long-term answer is to do an event-level permission check in the PHP, because it's not uncommon for someone to grant permission to edit only some events via an extension.