If the member races of the Dark Extraterrestrial Alliance do not believe in heaven, how do they interpret seeing their akashic records psychically? Do they see it is about themselves in prior lifetimes, or do they just think it’s about other beings who may have lives that resonate with their own current and presumed one-time existence?

You have summed up the dilemma and the oddity here quite nicely. It is the latter explanation that is the correct one. All of the akashic records are open to inspection. They do not expect to see themselves and if they do, it is not through great discernment but through varying levels of accuracy they still possess with respect to their intuitive reach. Because it is not divinely guided, it will be less accurate and there is no greater understanding within on their part that they are so like humans, that what is true for humans applies to them as well. They are quite in the dark about the true nature of the divine realm, so they do not believe in a divine origin of anything because they are atheists. So when they look in the akashic records and see similarities with what they might themselves tune in to, it is not with an expectation they will see their own story, but only similar stories of beings who have gone through similar trials and tribulations and it will have no larger meaning for them. Nor do they understand the workings of karma. They understand that rules are to be followed and there will be consequences for breaking them, but those are simplistic levels of thinking, and obvious sources of difficulty that are quite predictable. Their higher awareness of the spiritual nature of everything makes them blind to many of the loftier ideas about personal responsibility and divine ways of being as the answer for the difficulties in life, and how to create a just and balanced world that serves all fairly in a balanced way. It is only the spiritual beings who think such things and prize such ideas.