Hopefully I'll be able to answer you questions.
When an external party is explicitly invited to a group by their email address, when they accept the invitation and create the account using the same email address, two things happen: A Jive System Administrator needs to approve the user account, despite being explicitly invited by the group administrator
It sounds like moderation is enabled in which case, this can be changed two different ways; One way is you to disable moderation or the other is to only enable it for addresses matching the blacklisted domain list. This would remove the moderation requirement that is currently in place unless their domain is blacklisted.
secondly, a Jive System Administrator has to change these new users to a standard user for them to participate in the group.
Depending on whether or not you want the groups to be externally accessible or not, you can either make the group an externally accessible, this document goes over how to manage those groups Managing External Groups. Or if you do not want those users to be externally users but rather standard users, then all you would need to do it as their domain to the Community Domain List as shown below:
This document goes over Configuring User Registration
Hope this helps.