Whenever you use --times (included in --archive) rsync will fix
incorrect time stamps. The only thing --size-only is doing is keeping
the incorrect data instead of replacing it.
The purpose of these options is to "fix" a copy done in a way that did
not preserve timestamps but the data is known
When a file of same length already exists at the destination then the
command 'rsync --archive --size-only' (--archive is same as -rlptgoD)
may change the modification time of the destination file even if no
modification was made.
Type the following commands in a terminal in order to
