There is almost always a little red dot (I'm sure there is a more elegant name for it; I just don't know what it is) in the Creative Cloud menulet on my menu bar on both my laptop and desktop computers. My Creative Cloud Desktop app and my other apps like Photoshop and Lightroom are almost always up to date when I check this.
There has been at least 2 posts asking the same thing. Sorry don't have links to them handy.
Basically you have 2 options.
1) Find whatever update is causiing this, Can be a Notification or an actual Update of some type.
2) Stop the CC DTA from Opening/Starting when your system starts up and you Logon and shut down the Auto Updates. You do that in the CC DTA Perferences. you do not need that program running to actually use the other Adobe programs you have installed.
Then Restart your system.
If you are on a Mac IIRC there is a setting in the Mac OS X system for notifications and that can communicate with Adobe and popup a notification about the CC DTA so you might want to disable that also.