CB stores the email address in the Joomla user object, which also fires normal Joomla user store triggers. AcyMailing should be able to listen to those events and update the user accordingly. If it doesn't yes you could just act on the after user update and after update user triggers like the following example to check if email changed.
Global
Triggers: onAfterUpdateUser, onAfterUserUpdate
User: Automatic
Access: Everybody
Conditions
1: [var1_email] Not Equal To [var3_email]
I'm guessing you'll need to use the Code action with Method set to PHP then utilize AcyMailing API to update their AcyMailing user row as the AcyMailing action just subscribes/unsubscribes users to/from selected newsletters.