This plugin fetch all tweets from Twitter, which has been written about some of your posts. For new article are changes cheching every hour. For oldone it is question one or two days.
You can set how many tweets to show and in swich format. It can be regular HTML or embed tweets generated by Twitter javascript.
List of tweets is automaticky show above comment form, but your can also do manually by put funciont <?php tmip_show_tweets() ?> into your WordPress theme.
Just remember, Twitter allow to search tweets only few days old, so i will show probably only in new articles. Be patient.