What logically should've happened is that the explosion of Ceti Alpha VI would've been picked up by FTL telescopes as soon as it happened 15 years earlier -- or at least that Reliant should've detected the light from it as soon as it came within 15 light-years of Ceti Alpha. Destroying an Earth-sized planet would take an amount of energy equivalent to Sol's entire output for a week, so it would be an event that would outshine the star itself. Failing that, what logically should've happened is that the Reliant should've immediately recognized that one of the previously charted planets in the system was absent and replaced by a ring of debris, and that the planet they were nearing did not match all 6 of the orbital parameters recorded for Ceti Alpha VI.
What logically should've happened long before then is that the recovery of the Botany Bay and its passengers would've been made public and celebrated as one of the greatest historical finds of the century. What logically should've happened is that the Federation should've turned Ceti Alpha V into an official penal colony and monitored the Augments' progress closely while a gaggle of historians descended on the planet to interview them about the Eugenics Wars and other aspects of 20th-century history that had been lost in the conflict.
What logically should've happened when the Genesis Torpedo detonated in the middle of a nebula is that it should've done nothing because it was programmed to reconfigure the surface of an existing planet, not to build an entire new planet (and star?) out of diffuse gases. At most, it might've managed to create some microbes and algae that would quickly die in the void of space.
The Wrath of Khan is not a logical movie on any level.