Ron,
Thanks for the reply but it's actually not a redirect that's happening.
When I'm logged in as the Super Admin and roll over the domain's dashboard link in the My Sites pulldown menu, the URL shown is https://the-registered-domain-name/wp-admin, not the original subdomain.
I did create an A record at the the registrar pointing the registered domain name to the dedicated IP address of the Multisite installation; however, without that tweak, the domain mapping wouldn't work at all, correct?
Thank you,
Don