Hi,
Android KitKat has added restrictions for third party apps from modifying content on the external SD Card. You can find some more information here: KitKat and SD cards — what's fixed, what's broken and what's misunderstood | Android Central
So, every time you open a file from the SD card and add highlights to it, it makes a new copy of the file in /Downloads/Adobe Reader folder. This might be the reason that you see multiple copies of the same document. The workaround is to move the file to internal storage or once you have made a copy in the /Downloads/Adobe Reader folder, then access the file from this location for any subsequent operations.
Also, while deleting the files, did you delete the copies and kept the original i.e. the file on the SD card? This might help explain the reason you don't see any edits in the file.
Awaiting your response.
Thanks,
Adobe Reader Team