Gee whizz LH, we are talking about an experienced navy captain here. Joseph Burnett joined the Royal Australian Navy in 1913. By 1917 he was a Sub Lieut. on the cruiser HMAS Australia serving with the British Atlantic fleet. In 1924 we was the gunnery officer on the cruiser HMAS Adelaide. 1928 Lieut. Comm. on the cruiser HMAS Canberra. 1936 Exec Officer HMAS Canberra. 1937 Exec Officer on the British battleship Royal Oak.
Having served in WW1 he would have known all about the Q-Ships and their tactics.
If part of the Kormoran's crew abandoned ship all Burnett had to do was approach the Kormoran bow-to-bow or bow-to-stern. All armed surface raider's main armament was port or starboard firing. If Sydney had of approached the stern of K then she would have been out of K's arc of fire while her forward firing turrets would have freedom of action. If the K manoeuvred to get into a firing position then it would be obvious there was still crew on board. Sydney was then well placed to open fire and sink K.
Others here mention "100% assurance of identity". In war there's no 100% assurance. You make the best assessment you can and then open fire.
I cannot think of any noted military leader that required 100% assurance before acting.

JG/FME