I did also ask support at Mad Mimi the same question. I can't find their reply but essentially they said since the plugin was using the Mad Mimi API, double opt in is bypassed and the new record is immediately applied.
I think when the API is used the premise is that you already have the email address and relationship so no need for the double opt in.
We could, as website developers, not use the plugin and just use the form code generated at Mimi's to drop into our sites and get the double opt in to work.
I have not done that for the site I was referencing when I posted this question. But I have used Mimi code on another site previously and that works fine and provides the double opt in.