Twitter help needed

Hello everyone,

I need some help, so obviously I have come to the most obliging place. A user on Twitter has set up an account, which lets people with spare tickets for a certain football team's home fixtures hook up with fans after these tickets. I follow this user and get push notifications on iOS 7 whenever he retweets a notification when someone sends him a tweet. I am finding that this is too slow, with the tickets having already gone before the tweet has been retweeted. Basically I want to get push notifications when people mention this account. Is this something I can do on Twitter (I believe that it used to be)? or do I have to get something like Tweetbot ??

All advice will be very gratefully received.