I've just recognized, that Subtasks do not have the same Issue Type Security Level as the parent Issue.
In my case, I have issues of type task and a issue type security set to reporter and assignee, works perfectly. I have a huge number of tasks which i assign to other guys. Those guys can only see issues they are assigned to or they have reported.
Today the idea crossed my mind, to make subtasks to a parent task during a meeting. Now these guys cannot see the subtasks, but if a issue of type task is assigned to them they can access these tasks.