I believe that notifications are not generated in circumstances where you yourself take action. Perhaps that’s what’s going on in your case.
See this for a somewhat similar situation:
When one tries to use Asana for one’s own work, this really creates a a problem. We’re hoping that Asana will remind/notify us, but Asana is impeding this: It would work for another actor taking the action, but not ourselves. It’s also not clearly documented when such notifications are prevented which adds to the frustration. It’s true that some cases might be superfluous and should be filtered out, but not all of them. This is another example of a behavior that should be up to the Asana user to choose, I feel.
I don’t know of any workaround for getting notifications, but my workflow is not to rely on notifications for things like this, but it does rely on checking My Tasks, so you’d have to do that (perhaps even just leave a browser tab open dedicated to it).