When clicking on a user in chat, there are two "user profile" links provided. The first links to the chatroom user profile, but the second is supposed to link to the user on the associated site. But, in this case, it points to StackOverflow, not Mathematica.se.
This is by design.
The second link leads to the user's profile on the site they set as their parent site. For example, mine is Programmers, so the second chat profile link will take you to my profile there.
Users who first join chat from Mathematica will have it set as their parent site by default.
To change your parent site:
- Go to your chat user profile by clicking on your avatar in a chat room and using the first "user profile" link
- click [change] beside the Parent User field.