The settings in settings.php will override any configurations you (try) to choose in the Drupal UI: /admin/config/development/performance .
$conf['cache_lifetime'] = 0;
$conf['page_cache_maximum_age'] = 21600;
These two settings would override whatever cache timings you set in the Drupal UI.
The maximum_age setting (for example 6 hours) will display in your headers as:
After making changes to the max-age and clearing the cache, if you do not see the changes reflected in the Response Headers it may be worth looking towards nginx for the answer.
As per Q&A: https://stackoverflow.com/questions/19002567/nginx-add-header-and-cache-control .
It does provide good information about how cache headers are, or can be set in Nginx.