Steam under Parental Controls
Steam has an automatic updating system. Games, and even the steam client will update automatically, if you are connected to the internet.

What seems to be happening to you, is that one of the games (or the actual client) has registered its intent to update, but it cannot, due to offline mode being enabled.

Try enabling online mode, and updating everything. This should negate the need for an update, and fix the problem.

However, if I have read your question wrong, this method will probably not work.