How to make Posts/Blogs mentioning a user appear in the user's profile?
Step 1

Use the Message module to create "Messages" each of those mentions, similar to what is detailed in the answer to "How to get notifications in a new window when using the Mentions module?".

Step 2

Perform the steps explained in "How to allow users to manage their own Message Stack messages?", which can be summarized like so:


Create a flag (using the the Flag module).
Create a view 'Messages by user'.
Use Rules to flag/unflag messages.
Trigger the Rules Component to mark messages (using the VBO module).
Create notifications about Unread Messages (using the "Menu Badges" module).


Notes: 


Consider Step 5 as a bonus: whenever a new message gets created, the user gets a shiny notification in the format of an iOS-like (red) badge with the number of unread mesages.
No custom coding involved, only using some of the commonly used contributed modules (and "Menu Badges", a hidden gem ...).