In some rules (notably the Chinese Classical rules) declaration of Kong is allowed only after player has drawn a tile from the Wall (or Dead Wall, e.g., as a result of claiming a Kong).
Four Winds is more permissive in this respect since in most rule presets it allows the declaration of Kong whenever it is player's turn.
Related topics:
Kongs Hiding concealed Kongs
Kongs Kongs as concealed sets