So I'm pretty well experienced on PS4 and it's current position. So I would like to clear up a few things so you guys understand these issues you're having. You likely aren't having a actual issue with your PS4, but a miss understanding of what's going on based on what the PS4 tells you. It doesn't always label or notify you correctly. When I take my PS4 out of Standby (yesterday is a good example). I took it out Standby and when I started it up it said that BF4's update was added to downloads, I already got around to understanding this tho so it wasn't anything that bothered me. So to explain the process, when the console is in Standby (Sleep). It works updates, uploads, downloads and installs in the background (doesn't unpack or install system updates though). But when your system is in sleep mode it is actively open to any activated account to take advantage of. Making a situation where the system doesn't do anything but those specific things I've stated. When you boot back into your account, your system adds all the info to your notifications which makes things abit confusing. If the download is already complete and installed it won't tell you, but it will tell you it was added to your downloads, on the other hand if it's not complete during the time you go back on it will tell you when it finishes. Try going to your downloads right when you boot up, it will show you that the games already downloaded and installed. I also had checked this out a few days ago cause I had only one account till I added my old JPN one to get Onigiri and 4 games had updates while it was in sleep. Onigiri was the only one not done when I went back on but it was around 60%. All only said it was added to downloads tho. It's just so you keep track of what's downloaded I guess
