Invoices in Xero are marked as paid once they have a payment against them, its not a "status".
There are two ways to do that:
Option A — Mark as paid through reconciliation
When you reconcile an invoice and match it against the actual deposit in the bank feed, that will mark it as paid. This is our recommended way and what 90% of our customers do.
Option B — Send payments alongside orders
You can have Reconcile.ly send the payment too, and match the payment in Xero.
To do this change the send trigger in Reconcile.ly Settings to 'Created' then you can nominate a bank account to apply the payments to.
If you run into any trouble doing this, please don't hesitate to reach out to us via the Live Chat button at the bottom-right of the window.