On iOS how to view the tweets of a particular user in Twifferific and Tweetbot
In Tweetbot you can easily do it the following way: 

Go to the search tab and use the “Users with“ option. Than type type (or paste) the twitter handle (e.g. @BarackObama). At the top of te search results you find the profiel of that person. Tap on it and go to tweets.

This works quite similarly in the official Twitter app.