It depends by what you mean by "the fallout." The Tsar Bomba generated basically no "local fallout" — its fireball never mixed with the ground and so its fission products stayed in the cloud without "falling out" in the near-term, when they were most active. It did however contribute to "global fallout," which is to say, the cloud circulated in the northern hemisphere. This contributed to the general radioactivity in the northern hemisphere, and would have been detected for quite some time. However because of how it was designed, it derived almost all of its explosive energy from fusion, and so the amount of fallout was relatively low compared to other high-yield hydrogen bomb tests. As detonated, only about 1.5 Mt of its yield was from fission (which determines the radioactivity of the fallout), compared to, for example, 10 Mt of fission from the 15 Mt Castle Bravo detonation in 1954. Had it been detonated in its dirtier mode (100 Mt, with +50% from fission), it would have increased the total global fallout from nuclear testing by 25%. But anyway — the global fallout hit the ocean, sure. But there was basically no local fallout.

You may be interested in this explanation by /u/restricteddata about about how the bomb's shockwave actually helped reduce the amount of fallout generated by the test: https://www.reddit.com/r/AskHistorians/comments/1ukfqs/comment/cej5gcn

That same user, restricteddata, is the creator of Nukemap, which can be a useful tool to get a sense of the scale of nuclear weapons, which seems to be your goal with this question. There are actually presets for the Tsar Bomb test.