I can confirm that the domain shows up within the Addon Domains tool that you mentioned.
However the Add-On Domain Support article state that for newly added Ad-On Domains, “a new directory will be created in your account with a new htdocs directory so you can upload a different, separate website for the domain name.” Yet, when I view my File Manager, I only see the htdocs for my primary domain – there was no new directory created inside of htdocs for the new Add-On domain.