You should change archive to mark as read in the e-mail notification or at least give it as an option to configure in app settings. It is not God usability to open the app to mark them as read.
Just as it is possible to mark an email as read in the app, it should also be possible from a notification. Replace the option to archive the email or make it possible to choose actions.
When you click on mark as read, this should be reflected in the app and synced with the server.
It should be possible to choose the actions when looking at a mail in the notification area. Archive is not relevant for all users/markets. Mark as read should be possible to use directly in the notification.
This is not working as stated in the comment! There is no setting for this in the app. There is one option for notifications for e-mails that states "All" or "None". E-mails placed in sub folders are not producing any notifications even though "All" is selected.