When you want to prevent people from seeing anything but their own activity, Private Mode is what you need. Simple enable it for a board, and members will only see their own logs. They can still log collaborations, filter and export, but everyone else's activity will be invisible.
Even with Private Mode enabled, board administrators can see everything. This gives you the power to control who can see what.
To enable Private Mode, go to a board and click on its settings gear icon. There, enable Private Mode.
To configure Private Mode, you must be an admin.