To pull-to-refresh and manually refresh data from Salesforce, swipe down and then release when you see the spinning animation. If the app has internet connection it will retrieve updated data from the Org.
NOTE: The Axsy Emergency Response App has been configured to automatically poll for data every 5 minutes. However, this will only occur when the app is active and being used. The app will not attempt to retrieve updated data from Salesforce if the app is in the background.