I am confused, the library table should be per operating system user (after all it is in ~/.config/kicad). So how can the libs of one user appear in the one of the others? Is it possible you add the user specific libs to the project library table?
You might want to read:
If you however want all users to work on the same projects and have access to the same libs then make a special directory somewhere under /home/ where you give all users access rights (example by adding all users to the same group and give that group ownership). Then instruct all users to add these libs to their personal global library table.
By the way i made the assumption that you are under version 5 