Could it be that the NAS is setting the file data to the current time?
From FFS help file:
Most FTP drives set a file's time stamp to the current time when synchronizing ignoring the source file's time and date. As a workaround you can do a Compare by File Size."
Latest v6.8 has (finally) abandoned the "creation time hack" to handle DST and now you can set the delta by yourself. https://sourceforge.net/p/freefilesync/discussion/help/thread/33079e91/
Give it a try!
I'm pretty sure is something related to the destination time stamp, compare the fields manually to find out...
Here you are a "Synology" search on the FFS area, not to much entries...
A good one could be this: https://sourceforge.net/p/freefilesync/discussion/help/thread/4be34d11/