extract serialized array to use for wp-query

You need to unserialize() if its serialized string.

In your case from what I understand you store the array in the user_meta so its serialize it when you store it. but it will unserialize it when you use the get_user_meta so you dont need to unserialize()

Your code seems fine.

$author_in = get_user_meta($current_user->ID, 'following_users', true);
$first_post_ids = get_posts( array(
    'fields'         => 'ids',
    'post_type'      => 'the_posts',
    'author__in'      => $author_in
));