there used to be more planets in the Persean Sector, but they fell into disarray, and disappeared over time. That's where decivilized population and ruins come from. Hegemony was most likely stationed somewhere far away from Core Worlds, and their journey across the Sector to reach its centre added to the fact that colonies deeper in space died out. As it is described in their lore that they were scrapping key infrastructure on the way there to maintain their fleets.
I think that's what I read on the blog recapping the story.
You also need to remember that AI Wars decivilised a vast amount of colonies apparently, as the range of destruction by Hegemony and Tri-Tachyon was so immense, after all you can find various automated defences being outside the Core Worlds. Suggesting Tri-Tachyon wasn't always entirely based around the Core Worlds. And most likely Hegemony wasn't as well.
As of the direction the Hegemony came from, that could be entirely arbitrary, as the Sector is randomly generated with the exception of the Orion Perseus Abyss and stuff like that of course. But the Hegemony most likely didn't come from that direction (as you said), and I assume were probably stationed on some random systems far out unrelated to it.