Registration with MailChimp double opt-in
MailChimp audience has the option "Enable double opt-in". Enable this option if you want MailChimp add a new member to the audience after the email confirmation. You also should set options "Default From name" and "Default From email address".
[MailChimp > Audience > Settings > Audience name and defaults]
Note: MailChimp option "Enable double opt-in" has higher priority than extension options.
Ultimate Member settings
Ultimate Member has the option "Enable double opt-in" that can enable the "double opt-in" feature for a certain connection if it is not enabled in the audience settings.
[Ultimate Member > MailChimp > Edit audience]
The extension adds a new member to the audience after member approval. The extension doesn't add a new member if the member's status is pending admin or email verification until this member will be approved.
Look at the "Registration Status" option in the "Registration Options" metabox on the user role settings page. New users will not be added to the audience immediately if the option "Registration Status" is "Require Email Activation" or "Require Admin Review".
[Ultimate Member > User Roles > Edit Role]