I it's normal that your replies do not show up, neither do mine, I have posted several answers and they didn't show up as well, I don't know why.
Why do my replies on Twitter not show up?
Have you checked if your notifications are on in the settings of your phone? Also check and make sure that the settings in the app are set on.
You can adjust if you want to be notified when tweets, mentions, and replies are towards you.
It used to be that all of your tweets and @replies were shown in your timeline whenever you, or anyone else clicked on to your timeline, but then Twitter made some modifications...
Personally I prefer this view as it used to be annoying when you would go to someone's timeline and have to scroll through all of their @replies, which don't really have any relevance to anyone but the person they are directed to.
As Twitter develops it continues to evolve and improve, and personally, I think this feature is a big improvement.