Hi,
Have you tried using this
web.config key:
<add key="CMSStagingLogGlobalObjectsOnlyForAssignedSites" value="true" />
If true, tasks for global objects are logged only for the sites to which the respective objects are assigned. The default value is false.
However, when I am in CMS Desk of site A, make some document change, I see the task only in the Site A staging tasks area. If I log into site B CMS Desk, the task list does not contains this document staging task.
Best regards,
Juraj Ondrus