Most tools that sync files (in contrast to mere copies) need a way to know which files need to be copied, and which can be skiped. The expensive way is to perform a checksum, but most sync tools rely on the creation or modified date unless told otherwise.
Now say Alice and Bob have the same copy of file F, Bob modifies it first which gets stored at timestamp T, then Alice modifies her copy at time T+1.
Bob syncs his files on a filer, its timestamp gets reset to now, which is say T+2. Then Alice does the same, but her file does not get copied, since the remote timestamp T+2 is newer than her local timestamp T+1.
Now say Alice and Bob have the same copy of file F, Bob modifies it first which gets stored at timestamp T, then Alice modifies her copy at time T+1.
Bob syncs his files on a filer, its timestamp gets reset to now, which is say T+2. Then Alice does the same, but her file does not get copied, since the remote timestamp T+2 is newer than her local timestamp T+1.