Customer Lists are connected to Accounts/Teams. Unfortunately when you collaborate with other users who are not on the same team as you, their Customer List will not "sync" with yours. Their list will be completely independent from yours. This is to allow users on different Accounts/Teams to keep their lists private.
Unfortunately, this means that if an Outside Team member tags an Order with a specific Customer Code, it won't be linked to your Customer List at all. You would need to tag the Order with your own Customer Code after the order has been received.
The only way to share Customer Codes with another user is to move them into your Account/Team.