I'm a heavy user of the Twitter web and iPhone clients, and I'm not sure what you mean by "live updates" tab. Is that something in TweetDeck or another client?

If you (or parent poster ~TheTruth1234) found this unwanted, wouldn't unfollowing or blocking the source accounts be an adequate remedy?

(It is a embarrassing mess, but par for Twitter's lackadaisical approach software quality, that Twitter web often ignores their own settings' "don't autoplay" toggle, and has for many months.)