I read the Synchronization mode below which may be used in our case but this is not completely correct - to update the timestamp of the target file without comparing the file size. My suggestion is to initially compare the file size and if they are the same, go and update the timestamp. If not, the source file means it's updated and should replace the target file instead.
The you select the Synchronize timestamp mode, you will have an option Same size only.
Though the Synchronize timestamp mode is not really a solution, it's the last resort, when the server is buggy.