How to add user details to different tables immediately after user registration

Removing the table names from the column names when using $wpdb->insert() is what worked for me:

function add_to_affuser($user_id) {
    global $wpdb;
    $user_info = get_userdata($user_id );
    $wpdb->insert( 'mytbl_A', array('name' => $user_info->user_login, 
              'email' => $user_info->user_email ), array('%s', '%s') ); 
}
add_action( 'user_register', 'add_to_affuser');

function add_to_aff($user_id) {  
    global $wpdb;
    $user_info = get_userdata($user_id);  
    $wpdb->insert( 'mytbl_B', array('user_id' => $user_info->ID ), array('%d') ); 
}
add_action( 'user_register', 'add_to_aff');

While trying to reproduce the issue reported, I noticed that tables created using dbDelta() (and the database description provided) had lowercase names despite trying to use A and B. I was a little unsure of how the prefixes were set up based on your code too.

Here’s a demo plugin that includes the database creation part too. Custom tables are created upon plugin activation. The custom DB tables will be updated when adding a new user.

<?php
/*
Plugin Name: WPSE update custom tables when adding user
Plugin URI: http://wordpress.stackexchange.com/questions/241560
Description: 
Version: 0.0.1
Author:
Author URI:
License: GPL2/Creative Commons
*/

/**
 * Create the database tables upon activation of this plugin
 * 
 */
register_activation_hook( __FILE__, 'wpse241560_db_install' );
function wpse241560_db_install() {
    global $wpdb;

    $charset_collate = $wpdb->get_charset_collate();


    $sql_affuser = "CREATE TABLE {$wpdb->prefix}affuser (
        affiliate_id bigint(20) unsigned NOT NULL AUTO_INCREMENT,
        name varchar(100) NOT NULL,
        email varchar(512) NULL,
        from_date date NULL,
        thru_date date NOT NULL,
        status varchar(10) DEFAULT 'active' NOT NULL,
        type varchar(10) NULL,
        PRIMARY KEY  (affiliate_id),
        KEY status (status)
    ) $charset_collate;";

    $sql_aff = "CREATE TABLE {$wpdb->prefix}aff (
        affiliate_id bigint(20) unsigned NOT NULL,
        user_id bigint(20) unsigned NOT NULL,
        PRIMARY KEY  (affiliate_id, user_id)
    ) $charset_collate;";

    require_once( ABSPATH . 'wp-admin/includes/upgrade.php' );

    dbDelta( $sql_affuser );
    dbDelta( $sql_aff );
}


/**
 * Update affuser table after adding a new user 
 */
add_action( 'user_register', 'wpse241560_add_to_affuser');
function wpse241560_add_to_affuser( $user_id ) {
    global $wpdb;
    $user_info = get_userdata( $user_id );

    $wpdb->insert( "{$wpdb->prefix}affuser",
                    array(
                      'name'  => $user_info->user_login,
                      'email' => $user_info->user_email
                    ),
                    array( '%s', '%s' ) ); 
}

/**
 * Update aff table after adding a new user 
 */
add_action( 'user_register', 'wpse241560_add_to_aff' );
function wpse241560_add_to_aff( $user_id ) {  
    global $wpdb;
    $user_info = get_userdata( $user_id );

    $wpdb->insert( "{$wpdb->prefix}aff",
                     array(
                        'user_id' => $user_info->ID
                     ),
                     array( '%d' ) ); 
}