it seems they forgot to add a logout
If you are accessing the control panel from a normal Internet browser, then a formal log out ought to be unnecessary. Simply close the browser. This will lose the current browser session ID and create a new one when the browser is next opened. The new ID will need a new login.
If opening a new browser logs in automatically, then either the DD-WRT is ignoring the session ID or it has set a ‘keep signed in’ cookie or other marker on the computer.
I hope this helps.