Hello Richard. Unfortunately no, your certificate for your primary domain will not work on customer domains. Most email clients and mobile devices default to customer-domain.com, mail.customer-domain.com, or autodiscover.customer-domain.com when probing for account set up details, and so it is best to have these hostnames set up to terminate on the SmarterMail server, then implement an SSL certificate that can cover all of these required hostnames in IIS. A good way to go about that is using Lets Encrypt as you'll see here:
Kyle Kerst
IT Coordinator
SmarterTools Inc.
www.smartertools.com