Domain Mapping Add-on domains as New Sites breaks site wide user registration/login - Buddypress bre

I have primary domain hosted by bluehost with its dedicated IP, plus several Add-on domains hosted under same account.

WPMU set up on primary domain no probs, as a subdirectory install. And have followed
https://premium.wpmudev.org/blog/how-to-map-domains-with-the-wpmu-dev-domain-mapping-plugin/
to map parked (therefore pointing at my primary domain) Add-on domains as New Sites in my network.

So far, so good. The sites load correctly in Safari.

But it seems that, once registered, new users can log in only via the primary domain (i.e. the one on which the network is installed). Is this correct? Is there any way around this? I'd like them to be able to register and log in on any of the network's sites.

And, worse, somehow BuddyPress when network enabled seems to break the sending of user registration emails by WP entirely. The emails never arrive. This is really bad news for me since I was very much hoping to create a community using my primary + Add-on domains.

Help please!