According to Reddit user Forkrul, the message generally needs to be displayed in some way in order to be effective, however, "the notification can be enough depending on how much of the message it parses". As to how this is happening, the most likely cause is a character, or set of characters Sony's messaging system can't handle or acts on in some way that renders the console unusable.
Thanks to a new exploit being favoured by hackers online, Sony has issued a warning to gamers, urging them to set their messages to "PRIVATE" within PSN.
You can view the exploit message in the app too and it won't break your phone, but deleting it there still won't protect your console.
Users have discussed the issue on the r/PS4 Reddit board, where they say they are receiving messages to their consoles through the console's messaging application, Kotaku reported. The bug, in some instances, has been used during matches to cause the opposing team to crash and be unable to complete a match. The app is free on both iOS and Android, and it's an easy way to both delete messages and block users. It happened to me during Rainbow Six: Siege.
To adjust settings go to: Account Management - Privacy Settings - Who Can Message Me - Select "No One". That way, you won't accidentally trigger the bug, in case you're one of the potentially affected users.
The offending messages apparently have the word "Juegas" and a odd symbol that can't be recognized by the PS4.
We now return you to your regularly scheduled weekend.
So far, Sony have made no official statement on the matter, however outlets such as Kotaku, Polygon and others have sought comment or clarification from Sony on the matter.