Worried about missing important email? There's no need. The app's Badge Counter displays a counter of new emails on the app's icon. Furthermore, you'll get push notifications when new email arrives.
The app “pushes” new email to your mobile phone automatically when they arrive, so you don't need to do anything to make them appear in the Message List.
If you want to manually check for new email, then swipe down the Message List to “refresh the page.”