In order for natural carbonation to be formed the second fermentation must occur in the sealed bottle, not in the carboy. What might be confusing you are the terms "secondary fermentation" and "second fermentation". "Secondary" fermentation is when you rack the beer out of the primary fermenter in order to remove the lees and allow the beer to clear. Whats meant by performing a "second" fermentation is when priming sugar is added at bottling time to allow for carbonation to take place in the bottle. If you look at Pawns post you can see that he is adding the priming sugar at the time of bottling.