For per-user you'll have to use a field like you've discovered. Once you have the field created simply substitute it into the tab description and it'll display. See the below on how to use substitutions.
www.joomlapolis.com/documentation/279-community-builder/tutorials/18353-using-substitutions-throughout-cb
So for example you'd have the following as the Activity tab description.
[cb:userfield field="cb_activity_text" /]
If you only want this visible to the profile owner you can surround it with an IF condition as well. Example as follows.
[cb:if user_id="myid"][cb:userfield field="cb_activity_text" /][/cb:if]