wp_new_user_notification

Update, after doing more debugging.

Whenever a user registers for my site through the Chargify plugin, the e-mail containing their password + login information does not get sent to them, but the admin is notified.

Whenever a user registers for my site through (/wp-login.php?action=register), both e-mails get sent properly, to the admin, as well as the e-mail to the user containing their password etc.

I figured out the problem, and am now posting the solution for anyone else.

In the chargify.php file, the bug is located in
function subscriptionCreate()

Locate the code section that looks like this

if(isset($trans['existing_user']) && $trans['existing_user'] == true)
$user_id = $current_user->ID;
else
$user_id = wp_insert_user($args);

instead of using wp_insert_user we need to use wp_create_user

Simply change
$user_id = wp_insert_user($args);
to
$user_id = wp_create_user($email, $user_pass, $email);

I hope this helps anyone else with this problem.