The 10's were the middle of the wave of Indian teachers coming to US shores and offering the public a first glimpse of non-Christian spirituality. The catalyst was the Parliament of World Religions of 1893 [1], when Vivekananda came to the US. By the end of the 10's, Paramahansa Yogananda had come to the US to found the Self-Realization Fellowship, the Theosophical Society was reaching the height of its popularity. The Bahai movement was beginning to take hold, etc.

It was basically when Eastern spirituality first wove its way into the American consciousness.

[1] http://en.wikipedia.org/wiki/Vivekananda_at_the_Parliament_o...