I had the scoop on how Twitter's new algorithmic timeline works.
The algorithm that will re-order your timeline is based on the one that ranks tweets for the "while you were away" feature that Twitter introduced a year ago. The best way to think of the new timeline is as an expanded version of this feature. Spend an entire day away from Twitter, and when you open the app again, you'll see highlights from the day. If you open it up a few times a day, you'll see a handful of "while you were away"-style sections breaking up the chronological tweets. And whenever you pull down to refresh your stream, it's back to the regular, reverse-chronological timeline.