This almost seems to be a bug, since the Xero web interface works differently than the API.

In the "Tax" section for a Contact, the help message states: "Each account you code an invoice to will have a default rate as specified in the Chart of Accounts but if you have specified a rate for the Contact here, this rate will override the default rate from the Chart of Accounts."

This works when adding an invoice using the web interface, but adding an invoice using the API results in the wrong tax type and wrong calculated total.