At the moment the population growth of sites happens as with the player fortress by migrants arriving, the majority of said migrants are not real people but were simply conjured into existence in order to fill up the migration wave. Only historical characters reproduce in the normal manner and sometimes non-historical characters can get promoted into historical characters, such as when they kill a historical character or when they are given a government position.
Population in AI Sites is limited not by the population limit as with the player fortress but by the available food supplies. The amount of food produced in a site is determined by it's biome support, by the available types of food that the creature can eat (carnivores populations are always lower), by whether the creature is allowed to farm overground and underground and lastly by how many kinds of food producing professions it has.
Major sites (called markets) like a fortress which trade with lesser sites on an exclusive basis can import food from those sites in their orbit, allowing their population to increase beyond the level that they could based upon their own core resources. Goblins however do not have to eat, so their population is limited only by the hard-coded maximum population cap of 10,000 for major sites and 500 for minor sites. They do however still produce food, which results in them exporting that food and spamming all the nearby sites with troll meat.