Hi,
Where did you add the address custom field tag ?
Normally, you're supposed to do that with the "address format" setting under the Checkout tab of the HikaShop.
When you do that, it will add the modifications to the address_template.php view file for both the frontend and the backend.
What you describe seems to indicate that you've directly edited the address_template.php view file via the menu Display>Views, but only for the frontend, while the email from your screenshot is sent from the backend and thus doesn't have the modification.