In desktop you will see the sync option on the feature service capabilites (Add Update Delete Sync) or on AGOL when you go to the item page for that service and click edit you will see the sync option at the bottom of the page where you can enable editor tracking.Can you share the service with me an I can check it out.
Russ
Your server is 10.11. Sync is only supported on 10.2.2 servers and up. You will need to upgrade your server to get the sync functionality working on your on-prem server.
Russ
That is an ArcGIS Server service and not a hosted feature service. So the AGOL information will not be present on the feature service item page if you added the service to AGOL. The next thing I saw on the service is the editor tracking field CreatedBy. I took a look at the error coming back:
{"error":{"code":400,"message":"Unable to complete operation.","details":["Invalid column value [CreatedBy]"]}}
I am thinking this is happening because with editor tracking and the ArcGIS Server service is not secured which does not use the logged in name and it is trying to populate this field with esri_anonymous which is longer then the field you have set up allows. Maybe try to change the character length of the field and see if that works when you republish the service.
Cheers
Russ