Argonaut island (phantom island), Dagelet island (Ulleungdo) and Hornet island (Liancourt Rocks) in the map were not coloured.
But I recently found another version of the same map. It was from "Hammond's Atlas of The World" (C.S. Hammond & Co. N.Y. 1904).
(Please look at the left map) [Click the map to enlarge]
In this version, Dagelet island was painted in the same colour (pink) as Japanese land although Argonaut and Hornet islands (Liancourt Rocks) were not coloured. This may mean that the mapmaker believed that Dagelet island (Ulleungdo) was Japanese Matsushima while Argonaut island (phantom island) was Takeshima which was given to Korea in the late 17th century.
Please take a look at another map from the same atlas, the map of "China, Japan and Korea". (Please look at the left map) [Click the map to enlarge]
Argonaut island was not coloured again but both of Dagelet island and Hornet island (Liancourt Rocks) were painted in the same colour (pink) as Japan. And you may notice that there is a writing beside Argonaut island - "(Tako-simo)" which means Takeshima.
So the theory above may be right.
By the way, the subtitle of the atlas reads "A New Series of Physical, Political and Historical Maps Compiled from Government Surveys and Exhibiting the Latest Results of Geographical Research - Accompanied by an Index-Gazetteer of the Principal Towns of the World".
It is clear that the mapmaker of the authoritative atlas believed after the research that Liancourt Rocks didn't belong to Korea in 1904, four years after the Korean Edict #41 and one year before Japan's incorporation of the rocks (Takeshima).