@anjedeska,
If you do not want to send any mail, go to Mail Options and uncheck also there the standard WordPress email that is sent when a user is created or updated.
I have a similar question / issue about emails being sent when importing. I would like for emails to be sent with login information when imported. I have checked both boxes, chosen PHP Mailer, and added From Email / From Name. Import works but no emails are received. I even used the Send A Test Email option and it says the email was sent successfully, but I never receive the email. Any idea why or how to debug?
This is strange.
Have you tried to use the standard PHP mail and use also a SMTP plugin?
yes, i tried standard with no luck. i have not tried a smtp plugin, do you recommend one?
This is very popular: https://es.wordpress.org/plugins/wp-mail-smtp/
But any that works would be ok.