Image styles with $settings[‘file_public_base_url’]?

I deep dive in the settings.php file of Drupal 8.1 and try to configure $ settings['file_public_base_url']and $ settings['file_public_path'].

All media links are correctly rewritten, that works with static files, but styles fails with 404 errors as there is no php support and rewriting rules are not implemented.

How can you get styles to work with $ settings['file_public_base_url'] ? Is it related with Image cache external ?