Not particularly so it is depending on you. Your main login cookies would be cleared sure if you log out from your forum. However that does not mean that any session cookies stored in your browser like the catp cookie which stores a categories password would be cleared until you actually close that browsing session which is your case.
See you allow guests to see categories and your still in the same browsing session and the catp password exists which is why you can see the photos because you have the password stored.
Your users are presented with the password box for the cat.