What is the purpose of /Users/Shared/adi?
Apparently, these files somehow belong to the Mac App Store and the iBooks app. "adi" might be referencing "Apple Distribution International". Removal from the excluded Time Machine items is not recommended, as this behaviour does seem to be expected from all macOS installs >= 10.8 Mountain Lion.

Full explanation here: http://galvanist.com/post/66313155502/userssharedadi