Reading FAQs from Citi web page. Quoted below.
Q1. When do I start sending my payments to Citi instead of American Express?
A1: When you receive a statement from American Express please send your payment to American Express by mail, phone, or online. When you receive a statement from Citi, please send your payment to the address in your statement or make a payment online once you register for Citi® Online.
Q2. If I have a balance on my Costco card from American Express, will it transfer over to my new Costco Anywhere Visa® Card by Citi?
A2: Any balance on your Costco card from American Express account will transfer automatically to your new Costco Anywhere Card on June 20, 2016.
Now what if I have balance left over from Amex on June 20, 2016, to whom should I pay: Amex (according to A1), or Citi (implied by A2).
(Update 06-22-2016) Gave it a bit more thought, decided to keep the pre-scheduled full payment to the original Amex Costco, while adding a minimum payment to the new Citi Visa Costco. This way I would avoid the penalty if the Amex => Citi did not go through.
(Update 06-24-2016) So out of curiosity I actually posted this question to Citi via secured message. I received reply a few days later which appears stating they will do automatic transfer (from Amex to Citi).
(Update 07-02-2016) The payment went through (from Amex to Citi). A separate topic: it appears Citi did not give me 2% extra cashback for being Costco executive member (which according to the bulletin Costco just sent, it should). Anyway for me personally I will use Chase freedom (Visa) at Costco to get the 5% back (need to activate every quarter, which I did so far).
OK, I am reading the fine prints at Costco: Only purchases made by the primary and primary household cardholder on the account will apply toward the Reward. Since my wife made the purchase, so it sounds I won’t get the 2%?