The registered admin is notified as soon as a RegistrationMagic form is submitted. It doesn’t depend on the payment status. Automatic email or automation task’s email are sent to the users/registrants only, not the admin.
These tasks are executed on the users/registrants that fulfill the implemented settings under Payment status Rule, Payment processor Rule, etc.
The email is sent to the registered users and only to the users that fulfill the criteria at the time the task is run.

I can turn off automatic emails to admin after form submission. Then create an automated email for just successful payments. But that seems to only go to the person registering.

You can use the automation feature of RegistrationMagic to send email to the users when the payment is complete.

1- Go to RegistrationMagic > Dashboard for the form > Automation Tasks
2- Create a new task and name it
3- Enable Payment Status rule
4- Choose Payment Status as Completed > click on Next
5- In user account activation, choose Do Nothing > Enable: Send Email > type in the email and Save it.

To change the status of payments, please refer to the following steps:

1. Go to RegistrationMagic > inbox
2. Click on view for the submission that you wish to change the status of
3. Click on “Update” for “Payment Status” and select the desired status from the available options.

You can also set a custom status on the submissions to distinguish those with relevant identifiers in case the online payment processors are used.