Well before the events of the Battle of Endor (4ABY), the Transitory Mists were used by the Lorell Raiders as a hiding place. This gave them an advantage as the Transitory Mists are difficult to navigate and any route through them was kept in total secrecy by the pirate gang and the Hapan ancestors. It was also because of the Mists, that the Hapes Consortium were able to develop themselves in isolation.
This region of space finally opened itself during the Galactic Civil War, and begun friendly relations with the New Republic. After officially allying with each other, the Hapans shared their knowledge of the Transitory Mists
Because the Mists are a region of space, there is no ground battle needed to conquer all three Transitory Mists. At the start of each Galactic Conquest scenario that they are a part of, the Transitory Mists start with a powerful Hapan fleet at each. However, because the Hapes Consortium does not have an AI on the Galactic Map, the threat of being attacked by the Hapans is non-existant (with the exception of the conglomerate faction in Hunt For Zsinj), similar to the pirates in the Vanilla Game.
The Hapan fleet can easily be dispersed by an Imperial Remnant fleet headed by and Executor-class Star Dreadnought. All three Transitory Mists have a Heavy Frigate Shipyards, making them an ideal choice to attack early game. However, the Hapans preference to Ion cannons will make the battle a lengthy one as they'll be shredding even through an MC80bs shields!
In short, the Transitory Mists offer themselves as difficult obstacles but are very rewarding in return for this; giving access to more frigate manufacturing stations and access to the Hapan home worlds (Hapes, Charubah, and Terephon) themselves.