Final Cut Pro "Save Project In" does not immediately save all media

I've encountered this issue for a long time. When I archive my projects, I "Save Project In" a new library, on an external drive. Once I have completed that operation, the new (archive) library immediately shows up in Final Cut Pro. But when I inspect the hard drive I'm saving the archive library to, the size starts out very small (as low as 100MB for 30GB library), and grows over the next few minutes, or sometime over the next several hours. The new archive library will open fine in Final Cut Pro immediately, even if the size is very small in the hard drive. But if I try to open the archive library from the external drive on a different Mac too soon, there will be media missing. Sometimes I have to wait several hours for the size of the library file to finish growing. There is no indication within FCP that the saving process is still in progress, nor any indication when it has been completed. Since the size of the archive is always smaller than the original library, it's a guessing game whether the copying process has completed or not. I encounter this issue on both my MacBook Pro and my iMac. This seems like a glaring bug in FCP. Though I have never found anything on the internet about this problem.