If you have set up the automated campaign for first timers on the Dashboard, every new customer who enters their email address is getting that welcome email.

The customer has to open the email and click on the redeem link in the email to get a 6 digit code they use when they come in the next time. If you look at the customer on the Dashboard, you can see if they got the email sent to them. The activity section of the customer profile will show payments and any emails sent to them. It doesn't show if they opened the email or clicked on the redemption link, though. You'll only know that when they come in with the code.