It's been quite some time since the Team Builder was released but it hit the Garena server just recently. When I tried my first game on the mode with Diana it showed my progress towards unlocking the mage icon as 1 out of 5. So, I completed 5 games as a mage champ one after another and unlocked the mage icon.
League has been releasing a lot of cool summoner icons in the recent past and surely there's one for everyone's taste. Here's how I performed in that game which unlocked me the icon.
A little self praise here but I carried that 4 v 5 game like a boss B-) . Thanks for stopping by, good luck in the fields of justice summoners.