Rex Those apps you are referring to are file-based apps. They work on specific (usually small) files. When the file is re-saved, the whole file is re-written and would have to be synced to other devices.
Diarium works differently, it works on a database. If something changes in the database, it would be very inefficient to sync the whole database (because it could be multiple gigabytes large, with all the attachments).
I would not recommend changing/moving the sync files that Diarium creates. If you want to have those files in a dedicated "All apps" folder, I would recommend the OneDrive sync, which creates a "Diarium" folder in an "Apps" folder. That "Apps" folder you could move to another location (but I don't see why this would be necessary).
If the iCloud sync works for you, then what exactly is the problem? If the sync button in the app has the checkmark, then everything looks good, I would say.