Branded O365 single signon experience for "external" SharePoint Online users

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We are using a third party authentication provider to support our login process to O365 and SharePoint Online.
  1. When signing into our 'ourdomain' tenant:
    With internal users e.g., users that are not yet signed in are redirected to a MS screen where they are asked for their email address, followed by a screen with “taking you to your organization’s sign-in page”.
  2. With external users, such as, they are not redirected to our organization’s signon page.
Is this something we can configure so that external users are treated the same as internal users in this respect?
Also, the O365 login page branding only seems to work for internal users - that is, users native to our tenant.
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