Based on the description of your issue it sounds like there is one key piece of information missing. When the form is submitted you need to insert a custom meta value in wp_usermeta that will create a relationship between the new user and the corresponding custom post type. Lets call it meta_key = ‘user_post_id’ for the code example below.
This custom meta value can then be used on your author.php page to handle the split logic you mentioned above:
<?php
// get the 'user_post_id' from the 'wp_usermeta' table
$post_id = get_user_meta($user_id, 'user_post_id', true);
// start the split logic
if( get_post_type($post_id) == 'judges' ) { /* judges code goes here */ }
elseif( get_post_type() == 'submissions' ) { /* submissions code goes here */ }
?>
As an alternative to creating a relationship to a specific post, you could just set a ‘user_type’ meta key with a value of either ‘judges’ or ‘submissions’. In that case the code would adjust as so:
<?php
// get the 'user_type' from the 'wp_usermeta' table
$user_type = get_user_meta($user_id, 'user_type', true);
// start the split logic
if( $user_type == 'judges' ) { /* judges code goes here */ }
elseif( $user_type == 'submissions' ) { /* submissions code goes here */ }
?>