For a fully functional MAPI/EWS/EAS environment you'll need to meet a few requirements for each domain you're setting up: 

https://mail.customer-domain.com should terminate on the SmarterMail web interface successfully and with no SSL errors. 

https://autodiscover.customer-domain.com should terminate on the SmarterMail web interface successfully and with no SSL errors. 

https://customer-domain.com/autodiscover/autodiscover.xml should redirect to https://mail.customer-domain.com/autodiscover/autodiscover.xml

Additionally, you'll need an SRV record referencing _autodiscover._tcp.customer-domain.com and it should point to mail.customer-domain.com on port 443.

IMAP/POP/etc based autodiscover have similar requirements but won't need the HTTPS access to facilitate that connectivity. With that being said, different email clients will handle autodiscover in different ways and you may need to adjust your approach for that. You can find more information on this here: