I agree with you. I would recommend that they do it in the white on orange text box, like the downvote message for those under 2k rep (if you don't know what I'm talking about, go downvote something and see the orange box. Then, unless it deserves it, go un-downvote it. If you have over 2k rep, a) you should already know what I'm talking about and b) you won't see it.)
I would recommend that they use something like that, but have it say
"Click the StackExchange button for a menu of useful links"
followed by 4 message boxes, one describing each tab.
"The Hot Questions tab displays the most active questions"
"The All Sites tab contains links to all of the StackExchange websites"
"The Inbox tab shows you what you have recieved comments/answers on"
"The Notifications tab shows you edits, badges and privileges earned.
Those would be useful to new users, to be shown whenever they create accounts, and possibly in a future tutorial for new users.