You were correct, WordPress core made a change to the API starting in version 4.3.0.
Anyway, it was a pretty easy update to make to the plugin and I just pushed a new version 0.9.9 that fixes the problem where the new user gets a bogus registration notification email with “Password: both” and is unable to complete site registration and set a password.
So please update to the new version and let me know if it solves the problem.
Note that if you have any users who have registered and never set their password, they can still set a password by using the standard WordPress “lost/forgot password” function. So if you have a number of users like that, you could send them each an email to let them know there was a problem on the site and give them the URL to reset their password.
Thanks for the bug report! I gave you credit in the changelog.
I am going to file a couple of feature requests/patches with WordPress core because the way this API is implemented in WordPress requires unfortunate copy/paste coding to alter the notification behavior. The result is that when core changes the API, it breaks lots of plugins. Also, the wording of the initial “Welcome” email that new users get could be improved.