Account Category

All downloaded transactions will post to the AMEX liability account
You are only required to choose and post the other side of the transactions.

First, Click on the  downloaded transaction to expand the detail line for entry.
When you make a  purchase , it is easy, you will choose the expense account that represents the best category
for the purchase.  

For your specific question, you are asking about what to do with the payment of the liability.
In this case  so you would choose the bank account that the payment
came from so that the bank account balance  gets reduced.  You will find your bank accounts
listed towards the bottom of the category window.  
In the payee name, you can use a vendor name  called american express.

It seems more intuitive if you were to download the bank activity for your checking account
FIRST and code that payment in the Checking account FEED window to the american express liability
account.  Then when you open the American Express bank feed the transactiom will match and you wil not need to do anything.  

But it doesnt matter which you do first, it will match
in the other bank feed.

Linda Saltz, QBalance

I am unsure if that is what I should enter. The Bank is displayed under "Asset".
Should I select under "Account Cateogry"  -  Chase (Bank) ??

See screenshots please.

Those 3 items are payments made to AMEX from the Chase Account. But I don't know if by selecting "Chase Bank" under Account Category will it take the balance from there and apply the payment to the card ?
Capture.PNG

It seem to have worked, thank you  !