If the value of the Primary Key is identical for some rows in the two databases, SJA will ALLWAYS overwrite the target with data from the source. That's how it's supposed to work! Are you sure that's not the problem ?
SJA identifies the rows by PK and nothing else. It's been requested from time to time by users that there should be other options, and Ritesh has (a I remember) written here that they will look into that, but I'm not sure if there is any conclusion yet.
However I believe, that it should be possible to use any unique index. A timestamp could be part of such a unique (composite) index. Problem with timestamps however is that the format has changed from different Mysqlversions. So if not the server versions are identical, results could be unpredictable.