The Report Feedback was introduced in May 2015 as part of the “New player reform system“.  It uses a pop-up in the client to inform players that one of their recent Reports resulted in a suspension for a player.
It used to only appear for the player who issued the final report before a ban was issued. However this mechanic was changed and nowadays every player who reported a player who got punished afterwards can get Report Feedback [606, 499]. It's important to know that the Report Feedback is purposefully tuned down in order avoid notification spam for players. So not getting a Report Feedback does not mean the player didn't get punished .
Riot has stated that the New Tribunal will most likely include some form of report feedback, to enable players to see their contribution to making the community a better environment. 
Please keep in mind that with Lyte leaving Riot, the new Tribunal is speculative feature we have no up-to-date information about.
To create the Report Feedback feature, Riot had to review privacy laws across more than 15 different countries. 
A screenshot of the Report Feedback players receive in the client.
278 https://ask.fm/RiotLyte/answers/134527663810 ; Page 6
279 https://ask.fm/RiotLyte/answers/134527205570 ; Page 7
499 https://ask.fm/RiotLyte/answers/130943806914 ; Page 224