Profile submit API call does not add contact to goup or send opt-in email

When using the AJAX interface to perform a "profile submit" API call to add a contact to a mailing list, the contact is created but not added to the group and no opt-in email is sent.

The call is performed as follow, from a Joomla custom content module :

CRM.api3('Profile', 'submit', {
    "profile_id":    20,
    "email-Primary": 'someone@somewhere.com'
}).done(function(result) {
    console.info(result);
});

Both the profile "Add new contacts to a Group" and CiviMail "Enable Double Opt-in for Profiles which use the Add to Group setting" are set.

It does work when using the HTML form snippet from the profile (contact created, added to group and opt-in email sent), but not when using the AJAX API call.

This has been lightly discussed in CRM-13234, but there is no documentation on how to get the profile submit API to add a contact to a group and send opt-in emails.