It would seem White City Amusement Park was the same as the Alaska-Yukon-Pacific Expo or at least located the same place. (which was located within Madison Park) I saw one note of White City being open in 1909....

Then came plans for the great Alaska-Yukon-Pacific Expo, first planned for 1907 but postponed to 1909. The boulevard system (designed by the famed Olmsted Bros, in 1903) was developed in the area of the Expo site (the University Grounds) and old photos indicate that Madison Park was given new features of amusement rides plus a new name: 'White City Park', which was to the directories of 1910-11-12, and then vanished as did the amusement rides.

On May 28, 1909, Queenie the elephant escapes in White City, a short-lived amusement park located in Seattle's Madison Park neighborhood. A ruckus ensues and some slight damage is done before the elephant is recaptured.......

Farther up the lake, Madison Park's White City sat at the terminus of an electric trolley line from 1888-1911.