Where do my pushed tasks go in Asana?

By default they land in your My Tasks — the private list only you can see. Each Supernote list becomes its own section there, so your lists stay recognisable, and unfiled Inbox tasks go to the top of My Tasks (Asana's "Recently assigned") — or to their own named section if you turn "Use default inbox" off. Prefer everything in one project instead? Switch the card's mapping to "A project" and pick or create one (default name "Supernote Sync"); your lists become sections inside it. One thing to know: My Tasks is private to you, but tasks pushed into a shared project can be seen by everyone in that project — the card reminds you of this when you pick project mode.