The mention function allows you to direct a comment or talk response to a specific user and notify them in real-time.
To respond to someone in the comments section of a podcast, swipe left on the comment you want to reply to and press the blue "Comments" button, then write your reply.
Similarly, to respond to someone in talk, swipe left on the talk recording you want to reply to and press the gray "Comment" button, then record your response.
To reply to messages on your Notice Board, press the message you want to respond to, then write your reply in the box at the bottom of the screen.
You cannot tag people in the live chat.