To reproduce with STK demo:

• assign demo-project-editors role to peter
• become peter
• publish /demo-project
• you should find the pulse badge not increased and no new task visible in there. It gets refreshed only manually, e.g. if you forth/back switch tabs within Pulse.

Update:
The problem is that the LocalTaskDispatcherManager#getAllRecipients doesn't seem to resolve groups transitively.
So peter is member of 'demo-project-publisher' and transitively member of 'publisher' group: He should receive the task-event.
The reason why this works in the new demo is because the group was set up wrong in the first place. 'travel-demo-publisher' is not part of 'publisher' group but the publish-task is assigned to both groups.

The transitive group-member is working correctly when it's not triggered by the event, so it's implemented correctly there. This might help: TasksStoreImpl#findPendingTasksByUser or GroupManager#getAllGroups(java.lang.String)

See attached screenshots.