This map of Japan was published about five years earlier than the above map in 1895 with the TIMES Atlas.
It doesn't contain Taiwan which was given to Japan on April 17th 1895 according to the Treaty of Shimonoseki, so the original map may have been drawn before this date.
Anyway, in this earlier map, Ulleungdo was labeled as "Matsu Shima (Dagelet)" and painted in the same colour as Japan.
[Click the left map to enlarge]
So this earlier map has the same characteristic as many other western maps from the 19th century that Matsu Shima (Matsushima, Dagelet, or Ulleungdo) was drawn as Japan's island whilst Take Shima (Takeshima, Argonaut, or phantom island) was drawn as Korean territory (although Take Shima or Argonaut island was not drawn in this map).
This thought was derived from the maps made by Philpp Franz von Siebold.
The old Takeshima (originally indicated Ulleungdo) went to Korea after the Takeshima dispute in the late 17th century (1696) while the old Matsushima (originally indicated Liancourt Rocks) remained in Japanese territory.
So von Siebold misunderstood that Argonaut island was Takeshima which was Korean territory and Dagelet island was Matsushima which was Japanese territory. Liancourt Rocks were not yet discovered at that time. This thought remained in the maps in the late 19th century even after Argonaut island was recognised as a phantom and Liancourt Rocks were discovered in 1849. This map is just one of them - with Matsu Shima (Dagelet) as Japan's island.
In the earlier years, old Matsushima (Liancourt Rocks) was recognised as Japan's island and in later years after Liancourt Rocks were discovered in 1849 Liancourt Rocks were thought to be out of Korean territory because it located more eastern than new Matsushima or Ulleungdo. It seems clear that Liancourt Rocks (old Matsushima, or later Liancourt Rocks which were located more eastern than new Matsushima = Ulleungdo) had never ever been thougt to be in the Korean territory.