First, make sure your Billy account has Accounts set up for both the Credit Card and the Checking Account that paid it.
Next, when the payment is posted in the Credit Card's Reconciliation page, (it will be a positive number), click on it and select "Create another transaction", then Match.
Finally, head to your Checking Account, the one that paid the Credit Card, and find payment, you can filter my Amount if you have a lot of transactions. Then drag the CC transaction you just created from the right side to the top of the transaction on the left side and match them.
What you've done is create a transfer of funds, which is what a CC payment actually is.