I have two users on Adobe CC utilising the CC library. The Library has been shared between the users so they're using the same one. However, if a user creates a file with linked assets to the library, saves it, then the other user opens it, the links are broken.
You mentioned that you are creating a file which has linked assets and saving it into your library. I am not sure where the assets you are linking with your file are placed. So, I am suggesting if you can place all the assets you are using for your libraries in "Creative Cloud Files" folder and share these assets with the other user and then you create your file and link it with the assets placed in "Creative Cloud Folder" and see if that works.