There are 3 ways a user receives an alert notification: Cyclops notification center, email and SMS. Below is some extended information regarding each medium.
Notification center: As long as the user is included in the alert recipient list, by default the user will receive a notification whenever the alert is triggered.
Email: Only if the email function is enabled on the Recipients section of the alert.
SMS: Only if the email function is enabled on the Recipients section of the alert AND the recipient has verified the phone number.