Drupal Commerce integration: Paid vs. not paid

We have a Drupal7 site integrated with ShipRush, and need some help with configuration / settings.

Currently all Commerce orders, whether payment status is pending (such as "pay by check") or paid (such as credit card authorization is complete) appear in ShipRush under "Waiting on Payment." No orders ever appear under "Ready to Ship."

So, we can't tell if the order is actually paid and ready to ship.

Shouldn't unpaid/pending orders appear under "Waiting on Payment," and paid orders appear under "Ready to Ship?" Or is there some other way to tell if the customer has paid yet?