I would suggest you change the "default rule" to "Allow the devices access to Exchange", this is a Global Exchange Rule which may cause issues and will affect devices outside the scope of your Intune deployment. Also note; Intune synchronizes EAS devices from Exchange - if users have previously EAS enabled devices they will appear in the Intune console, considering you have Default Rule to Quarantine this will definitely affect the users.
I will summarize my suggestions:
Change default rule to "Allow the devices access to Exchange" (No worries, everything will work as expected regardless, this is just a Global Exchange Rule targetting users outside your Tenant).
Make sure you deployed Email Configuration Profile for Gmail through Android for Work settings and that the user receives the configuration.
Yes, the Outlook application will appear as it's own device. Unforutunately the Outlook client is not yet supported with Exchange On-Premises. Microsoft has announced they will support it in UserVoice:
I'm having a similar issue where the device shows up in Intune twice, once as Android and once as Outlook. I'm using O365, and Intune with hybrid mdm, nothing on premise. I do have EAS set to quarantine new devices until we approve them. Would turning that off solve the problem?