Okay, here is some more information.
When on the client, click on Playing Now>Playing from [your server library name]>[your server library name]. On the right you will see information about the library, including the line (using my database size as an example);
Size: 36797 files; 22.9 MB in library; 432 MB in thumbnails
Using that information I was able to identify Thumbnail cache of my the Server Library, stored on the Client. See attached image of the directory. Note that all files in that directory add up to 432 MB, as per the size above. That is how I know that is the Server Library thumbnails. The other directories are older and smaller.
I suspected that when a Client opens a Server database, only the library is sent across, which is quick as it is only 22.9 MB in my case, and that the Thumbnail cache must be sent across at some other time. I suspected that because when I first checked the cache, the file "Date Modified" showed as 7:52 am on April 21st, while it was actually 9:53 am on April 22nd here at the time.
Just to test, I closed the Server library again, and reopened it on the Client. The thumbnail cache files were updated immediately. So, my suspicions were wrong. Although my observation would seem to indicate that the Thumbnail cache isn't updated every time the Server library is opened on a Client.
I guess we need a developer to explain when the updates are done, or why a thumbnail on a Client may not match the thumbnail on its Server.
Or someone with a known thumbnail mismatch could try closing the library on the Client, backing up the Thumbnail cache for the Server library somewhere, then deleting it from the directory, then open the Server library again and see if the thumbnail cache is immediately rebuilt, and if the thumbnail mismatch is fixed.