Samsung Galaxy S4 mini, Android 4.4.2 -- I get a nice clean notification with the person's avatar which I assume is the direct push from the Twitter app. I also get one preceded by a number (4040) which is usually a compilation of multiple tweets in one chunk. I'm guessing that one is coming as a text...dunno. I looked at all the settings but there are too many combinations that aren't too intuitive. My preference is the clean, single notification with the avatar.