I have experienced the same issue and could not get the connector to register a "task completed" event from Asana, UNLESS it was running in test mode. This is obviously unacceptable and renders this unfit for use in any workflow.
I seem to have found a partial workaround though:
Since I noticed that if I log out and back into powerautomate, it would trigger from the next or previous event, I wondered if this was somehow related to my user account status, so I shared the flow with a colleague, and it no longer appears under "my flows". Now, it does seem to pick up events from asana that are happening outside of a test run, but from what I can see it might not be triggering based on all of them (but this maybe due to some some caching or throttling of events because I am toggling the "completed" state to fire my event)
