Groups allowed to see publication tasks in the workflow are listed under config:/modules/workflow-jbpm/tasks/publish/groups. All users which directly or transitively have a group listed there are able to access those tasks.

However, if the matching group is only connected to a user indirectly, i.e. through another group, refreshing of the pulse indicator and the task list doesn't work properly, resulting in the same symptoms as described here: https://jira.magnolia-cms.com/browse/MGNLUI-3453

Steps to reproduce:

1. On demo.magnolia-cms.com, in Security, open the travel-demo-editors group dialog
2. Under "groups", add travel-demo-publishers
3. Log in as "eric" (has group travel-demo-editors)
4. Open Pages app, mark any page and click "publish", confirm
5. Observe how the pulse indicator number doesn't change
6. Click pulse, observe how the new task isn't in the "New" list
7. Switch to another tab and back to "New", now the task is there