How does science fiction/horror author create an alternate reality as a way of exploring issues of his own day and time?
I think we can best understand how to answer this question if we understand what "allegory" is. For example, in Star Trek: Enterprise, the crew is living hundreds of years in the future compared to us. However, in the third season, Captain Archer was constantly tempted to violate his values in order to obtain information about an alien race known as the Xindi. The Xindi had attacked earth without cause and now Archer had to find and stop them. At the time, the US had recently been attacked and our president was calling for a second invasion. Anyone that made that connection between America and the Enterprise was not doing so accidentally. The show was "allegorically" discussing current events, but the distance between our time and the future allowed the producers to dramatize the discussion.
Science fiction writers typically create worlds in which the injustices of the present society are magnified and taken to what the author sees as an inevitable conclusion. To that degree, there is really no alternate reality, simply an alternate setting for the current reality.
Kurt Vonnegut's "Harrison Bergeron" is an example of the author's fear of diminishing the gifted to equalize or level the playing field for the less gifted. The story is an exaggerated reflection of reality.
Though their settings may seem outrageous and distant, science fiction works generally reveal a recognizable and recurrent problem in society and human nature.
In many ways, some of the most powerful aspects of Science Fiction is its ability to create a reality that allows the reader to examine practices in their own. For example, Ursula LeGuin's "The Ones Who Walk Away from Omelas" is a short story that explores the relationship of social construction of power in a mythical land called Omelas. It has much in way of our own social order's understanding of power and the dispossessed and how both interact with one another. Bradbury's short stories and extended work do much of the same, as they analyze social settings in an extreme, which on first glance, one would dismiss as "improbable." Yet, upon further analysis so much of what is done in these settings is done in our own world. Slesar's "Examination Day" is a short story that hits the reader right where it hurts in terms of "assessing intelligence" and in doing so helps bring ethical issues about testing, intelligence, and government control to light.
The key to good sci fi is the author's ability to create a compelling and rich alternative universe. Asimov was particularly good at this and he gave up his universe to other budding writers to use for their own work. By creating a believable universe, an author can manipulate it to convey their argument. Haddix creates a world in Among the Hidden where third children are not allowed and uses it to create a larger argument about government influence in every day lives, conspiracy, and food production.