No, the exclusion is of press and public not of Cllrs.
They are bound not to divulge that which is conducted in closed session - so long as that which is conducted in closed session is appropriately required to be, and qualifies, as being withheld from the press and public.
If there is business conducted in closed session which should not be, then the situation flips and any member NOT disclosing that which is not properly qualified as confidential are breaching the CoC for improperly preventing someone access to that which they are entitled to access.
Moral of the story - use the privilege of exclusion wisely and carefully.