CB Conditional does not and may never work with CB Core Fields Ajax. CB Conditional for display outputs completely removes the content. It doesn't exist to display. So the content would still have to display, but be hidden in the DOM; this potentially means tabs like CB Gallery being available when they should not be. Next CB Conditional would have to listen to CB Core Fields Ajax events and match it to a fields condition to execute. It is unlikely this functionality will ever exist, sorry. The best I can suggest is a refresh of the page after an ajax edit using some jQuery listening to the elements cbajaxfield.update.success event.