Do they not update automatically ?
No. You have to choose to download new releases. However, you should see them in the CC Desktop App list. As F.McLion says, you may have to sign out of CC and sign back in again before the CC app notices that new stuff is available. It's not the smartest kid on the block.
I was able to get to the CC app list and updated (downloaded) LR CC. However it does not appear on my computer. I have restarted computer and when chcking the CC app list it shows that I have downloaded LR CC - what am I missing?
Update -- according to CC app list I have updated
1. PS CC
2. PS CC (2014)
3. LR CC (2015)
4. Bridge CC
None of the above updates appear on my computer. What does show up as modified today is an old app ADOBE LIGHTROOM. However when trying to open this app it flashes a photo for a split second then disappears. It will not open. I am hesitant to start uninstalling apps as CC says all have been updated and I would have no way of reinstalling the apps.