I think this refers to handling JSON ActivityStreams objects at the `/outbox` endpoint for a logged-in user, and then broadcasting those out appropriately. If so, then yes that's the only API that's used. It also handles the uploadMedia endpoint and a few other details that are included in the spec.

I have tried unsuccessfully so far to set up an OAuth provider server along with it, so that you could log in on your phone, etc.

That is great news, one of the few implementations that does it. :D Do you have a demo server set up anywhere? Mine (based on my own activitypub code) is at https://federated.id :D