The carriers that you have setup in your StarShipIT account need to be added under Settings -> System -> Shipping Companies in your Unleashed backend for the orders to update correctly.
For example, if you have 'Australia Post' setup in StarShipIT, you will need to add 'Australia Post' in Unleashed.
Q: What status will the order be marked as after the update?
A: Orders will be set to 'Complete'
Q: Can you process the orders as partial shipments?
A: Partial shipments are currently not supported by Unleashed