The issue sounds like a bug. You're right, clicking the "Configurations" icon in the application list doesn't trigger Push messages (the method responsible for it is ApplicationResource.java:updateApplicationConfigurations()). We will fix it in further version, but this may take time.
The Push message is sent by the backend, not by the frontend (is called by the Java code of the server component). See, for example, DeviceResource.java:updateDevice(), which is calling pushService.notifyDeviceOnSettingUpdate().
A correct Push message notifying Headwind MDM on the configuration update and processed by the launcher is configUpdated.
A message of type appConfigUpdated is sent when application settings are updated. Since it doesn't affect the Headwind MDM launcher, it is not processed by the launcher. Third party apps can subscribe to receive this message - it means they need to refresh their configuration. See for details: https://h-mdm.com/headwind-mdm-api/