When setting up a sync relationship between two servers that have multisite, a site dropdown option becomes available that is not present without multisite. This site dropdown can be the difference between content moving or not.
For the first sync which creates a sync relationship between servers make certain to select the "all folders" option in the site drop down. After the sync completes for the "all folders" site option you can create additional sync relationships for your various multisites. Please note that a multisite sync relationship will still sync the whole database and is mainly useful for syncing templates for specific multisites.