The pilot of an amphibious Cessna 206 had been chartered to fly two passengers from an aircraft landing area at Warnervale to Berowa Waters on the Hawkesbury River. A gusty 20 kt westerly wind was blowing in the Warnervale area at the time of aircraft departure. The pilot recalls being concerned about making an approach into Berowa Waters and encountered turbulent and uncomfortable weather conditions enroute. After making a normal approach to the landing area, the pilot closed the throttle and flared the aircraft. As the floats touched the water, the aircraft tipped forward and the nose of the aircraft dived under water, which caused the windscreen to shatter. Water flooded the cabin and the aircraft came to rest inverted. The pilot and the two passengers were not seriously injured and evacuated the submerged cabin through the door on the left side of the aircraft. Immediately following this occurrence, the pilot observed that the float mounted landing gear was in the extended position and not correctly positioned for a water landing. He cannot recall any actions specific to the landing gear following the departure from Warnervale or on arrival at Berowa Waters. Following recovery of the aircraft to dry land, the landing gear selector was observed to be in the neutral position.