I think you may be misreading the article. Jeff Cooper didn't invent the state of mind he calls "Condition White", he just invented the term, and I linked to it because the terms are convenient in explaining surprise. When you're reading a book in a library, and suddenly werewolves charge in and attack you, only a very special kind of person (Alert) is able to instantly transition to deadly-threat mode. Everyone else is caught in Condition White: no threat expected, mechanically "surprised" and unable to take reactions. However, if you're already in Condition Red (regardless of whether or not you call it by that name) and ready to kill some goblins at the slightest provocation, having somebody else charge you from the side will not catch you psychologically unready, so you won't freeze up, and you still get to act on your turn as normal and you get reactions. It doesn't matter if that "somebody else" turns out to actually be a third party who will kill goblins as well as you. In game turns, you were aware of a threat, so you are not surprised.