If you've uploaded at least one video, its YouTube link is now included in the tweet, so that the video shows up in your stream. This is supported at twitter.com etc, but not in e.g. TweetDeck.
Note that if you've posted both a video and a picture in the same message, only the picture will show. This is a limitation in Twitter, so in that case Twitizer skips the video link to maximize how much text can be shown in the status.
Note that the link to the message at Twitizer is always included, no matter what.