I've been testing the updated Domain Mapping plugin lately to figure out why the admin bar won't show on the front-end for sites with a mapped domain when users login with the original domain (subdomain).
It seems that the CDSSO message (i.e. "You have logged in successfully. You will be redirected to desired page during next 5 seconds.") is only shown when logging in from the mapped domain, not with the original domain (subdomain). I assume when this message is shown, it's ensuring the cookies will work cross-domain, correct?
To test this, in the Network Domain Mapping settings set Admin/Login mapping to "domain entered by user" so both the original and mapped domain work. Then try logging in at /wp-login.php for the mapped and unmapped domains after clearing cookies. You'll only see the message when logging in with the mapped domain.
I've tested this multiple times on separate installs and I'm using WP Engine as a host.