When performing a manual or scheduled sync in versions earlier than 9.2 the last sync time may show a different time than what is displayed in the server's time or the local machines time.
If the server leveraging the sites is running an Ektron Windows Service running on version 9.2 then the issue is likely caused by how the later version of the service handles time zones. The 9.2 version of the service will always calculate the syncs on UTC time as opposed to the server's time zone settings.
This is a limitation of leveraging the 9.2 Ektron Windows Service on earlier versions of Ektron. To get the last sync time to display as expected an upgrade to 9.2 would be required.