Auto Actions Trigger question

I have an auto action that I need to execute:

- When user presses "register" button
- Any time the user has edited his profile
- Some of the profile fields a user is allowed to edit are ajax text fields. Do they fire a trigger (and if yes, which one) when they get edited on profile or on user list? If they do not fire a trigger, how to execute auto actions in these cases?

- When user presses "register" button
- Any time the user has edited his profile

Use the after registration and after profile update triggers. You can't perform an action directly when the button is pressed, but instead need to perform the action during the PHP behavior.

- Some of the profile fields a user is allowed to edit are ajax text fields. Do they fire a trigger (and if yes, which one) when they get edited on profile or on user list? If they do not fire a trigger, how to execute auto actions in these cases?

If using CB Core Fields Ajax then yes they do fire the before and after profile update triggers.