Ok...is there a specific game you've been playing? It's possible it's that individual game. That was the case with Sound Shapes. From what I'm reading, it's incredibly rare for trophies to pop without a timestamp on the PS4. The only instances I can find of it occurring are from A: Specific games that will require a patch to resolve the issue, and B: Hacked trophies.

I have this problem when i started playing uc lost legacy and right know with wolfenstein 2 and re 2 After i update my pro to the newest firmware 

There are even trophies in this games that habe a time stamp but some not and im worried when i sync my trophies Sony will ban my account even i get all my trophies legit