By default your Authorize.net account is configured to send email receipts to your members when a charge is processed. You can disable this or customize those emails from your Authorize.net account settings.
First log into your account at https://account.authorize.net.
Next click on Account -> Settings:
Next click on Email Receipt:
On the Email Receipt screen you can disable the email notifications or add custom headers and footers — information that will be prepended and appended to the standard Authorize.net transaction receipt respectively.
Note: Member Splash pre-fills the email address of the billing contact when payment is made if there is one saved to the account. The member has the option to enter a different email address or delete the field. Obviously no receipt is emailed if no email address is provided.