This sounds a bit odd since Your Library should be synced up on all your devices.
If you don't see the songs you've added to a playlists on your PS4 syncing up to your phone, we'd recommend logging out and making sure you log back in with the same username and password as you've used on the console.
It's possible that you have 2 different accounts and that's causing the confusion. Take a look at this page to see how to see how you can locate another accounts.
Keep us in the loops here and let us know if you have any other questions.
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