After I created the user story in devops, and I marked it both with Iteration Path and a tag for a corresponding iteration already syncing with Avion, this new story got imported into Unplanned iteration in Avion. I believe it should sync into corresponding iteration.

It will also be good to fix the other bug I submitted that Iterations synced from Avion don't go into corresponding iterations in DevOps and are just marked as tag, which require a manual step to assign them to an iteration...