To my knowledge, neutrinos are not generated during the fission process - just fission products (two nuclei), neutrons and gamma rays, and photons from X-rays to infrared as ionized atoms regain electrons (recombination). The neutrinos come afterward from the beta decays of the fission products - and that would be seconds, minutes, hours or days later (depending on the radionuclide).
In a nuclear weapon, the fission reaction is over in a matter of microseconds, as it is prompt supercritical until the fissile material is dispersed (it vaporizes).
Besides - neutrinos have a very low cross-section for interaction with matter.