Install CB Core Fields Ajax, then set your fields to be Ajax capable on profile view, now install CB Content Module, then substitute in your now Ajax capable fields into the module using the below formatting.
[cb:userfield field="FIELD_NAME" formatting="div" /]
You can even substitute in entire tabs using the below usage.
[cb:usertab tab="TAB_ID" user="#displayed" formatting="divs" /]
Then you should be able to edit the fields directly from the module. Since CB Core Fields Ajax still fires normal profile update triggers then you'll be able to use CB Auto Actions just fine if acting on those triggers.
For more information on substitution usage please see the below tutorial.
www.joomlapolis.com/support/tutorials/107-use-cases/18353-using-substitutions-throughout-cb