Below is a link to an 1877 Japanese map that shows "Takeshima" (竹島) as Korean territory, but "Matsushima" (松島) as Japanese. However, the island the mapmaker believed to be Takeshima (Ulleungdo) seems to have been the non-existant island of Argonaut, while Matsushima seems to have been the real Ulleungdo. At the time, there was confusion in Japan about the location of Matsushima (松島), but this map is evidence that regardless of its location, Japanese associated the name Matsushima with Japanese territory.
Click on the link and then click on "1" to see the overall map, and "3" to see the closeup view of Takeshima and Matsushima.
Link to the Map