Ok, so the error was that PSNTL has the platforms in the game's and trophy's URL's. A multiplat game would have an URL with something like "mygame-ps4-ps3-psvita".
Now, if a game that's only on one platform releases on another one, sharing the trophy list, PSNTL will modify the URL, adding the new platform to it.
This fucked up the app, since it would think that that's a new game and it calculates the earned trophies as new ones.
I knew this issue and my app should handle it, but I forgot to correct the trophies' URLs. That was the reason for the double plats and the over 100% completion rates.