Yes, the app will sync in the background to keep you up-to-date. By default, changes will auto sync from the web app and the Android app; these changes push to keep your tasks in sync.

If you don't want to wait for the auto sync, you can perform a manual sync:

1. Scroll down on a task list, a details screen, or the left menu when they are scrolled to the top until a spinning icon appears.

You can change your sync settings on the Settings screen.