A short answer is that Charles Taze Russell, who started the Watchtower movement, which became the contemporary Jehovah's Witnesses, was heavily influenced by Adventism. On the question of annihilism and conditional immortality, both movements were directly influenced by the theology of George Storrs, a ex-Methodist minister who became one of the leaders of the Second Adventist Movement and who also became one of Russell's mentors, publishing some of Russell's early writings and even asking Russell to speak at his funeral. Storrs, in turn, was influenced on the subject by Henry Grew, a British-born minister living in the U.S., who was forced to resign his pastor position in the Baptist church for his teachings on this subject. Grew's writings found their way to Storrs, who then championed them to the leaders of Adventism and later to Russell. [1,2,3]

Storrs' sermons on the subject were published in "An Inquiry: are the Wicked Immortal?: In Six Sermons, Also, Have the Dead Knowledge?" which can be downloaded for free here

There is a deeper question here requiring a longer answer that I'm not qualified to give: why did this theology resonate with people in the northeastern U.S. at this time? One partial answer is that spiritualism was very popular during this period and was a direct threat to the church. The argument that souls were not immortal (unless saved) directly contradicted spiritualist views about ghosts/spirits. [3] However, I don't think that alone is an adequate answer and would love to hear additional theories/opinions on this subject from people with expertise in this period.

Sources: [1] George D. Chryssides. Jehovah's Witnesses: Continuity and Change. (Routledge, 2016)

[2] M. James Penton. Apocalypse Delayed: The Story of Jehovah's Witnesses. (University of Toronto Press, 1997)

[3] Malcolm Bull & Keith Lockhart. Seeking a Sanctuary: Seventh-day Adventism and the American Dream. (Indiana University Press, 2007)