How can I tell if my game saves are backed up?

Solution 1:

You can check which games have been backed up, manage your backed up files and restore save files from online storage by selecting (Settings) > [Application Saved Data Management] > [Saved Data in Online Storage] from the cross media bar.

If you are a PS+ subscriber and you have an internet connection your PS4 should automatically back you all your save files to online storage. It will only inform you if there is a problem with the process, such as no more storage space or a failed upload.

I don't think there is currently an option to turn on notifications for successful back ups but I am currently away from my PS4 so I can't check. You can see what notifications are you will receive from the following menu (Settings) > [Notifications].

Source - PlayStation 4 Online user Guide