Limit posts per author role (excluding admin) in home page

If I understand your problem then this should definitely work.

<?php 
get_header();

$users = get_users( array( 'who' => 'author' ) );//get all the users with author role in an array


foreach ( $users as $user ) {   //travers the array

    if($user->caps['administrator']==1)continue;     // skip the user if user also have administrative capabilities
$query = new WP_Query( array(
                            'posts_per_page'=>1, 
                            'author' => $user->ID
                            ) 
                    );
if($query->have_posts()):while($query->have_posts()):$query->the_post();

get_template_part('content', 'postlist'); 

endwhile;

else:
get_template_part('content', 'none'); 
endif;

} 

get_footer();
?>