He should have used --link-dest= on his rsync.

    PREVIOUS_BACKUP=$(cat ./prev_backup)
    NEW_BACKUP=$(date +%F_%T)

    rsync --link-dest=$PREVIOUS_BACKUP /path/source /path/dest/$NEW_BACKUP

    echo $NEW_BACKUP > ./prev_backup

This will copy /path/source to /path/dest/$NEW_BACKUP (which is a time stamped folder). But it will take into account the previous backup. If a file hasn't changed, it will create a hard link. If it changed, it will then copy the whole file.

And that's it.

Since it's the name is a time stamp. When you need to restore, just read ./prev_backup or just list the directory content, sort it and read the last entry.