there is a refresh button and a widget on screen,
1. i add a task from web app
Pls confirm it will not update in mobile android app till i click refresh button.
If you stay on your current view, and nothing is done or touched, then it will not update unless you click the refresh button.
This being said, if something is completed, postponed, added or pretty much anything is done within the app, it will then refresh itself and receive the changes made.
So in the simplest explanation, yes it does auto update, it just requires certain things to happen within the app.