So it's normal you don't see a YaNC tab on user profile.
It's great it doesn't show up on the public profile but when I am logged in, I would love to have another tab for it, like I do for the forums. The forums tab allows me to see my forum subscriptions, it would be really handy to have another tab that allows me to see my Yanc subscriptions... I played around in the tab management.. I used every configuration for setting Yanc but it seems to ONLY show up in UPDATE PROFILE. Weird thing was that if I set it for example as "left" is moved other content to clear the left area but nothing showed....
It's so by design (you need to edit php code to change this).
We try to make the user profile look same for the user himself as for others (only exceptions are small additional icons or upload/reviewing tools), so that user knows exactly what others see. The rest of the stuff is in the Edit Profile workflow.
Maybe this helps understand the logic behind the User Interface, for what it's worth.