Ok, there was some miscommunication. That is on me, I fully accept that I did not confirm that we were on the same page. DAoT stuff requires a lower tech form to research even for the Homeworld. Atraxas cheats due to having the Ad Mech on hand, but the Homeworld requires an understanding of a more simplified version of a given technology to complete a research project.
In this case even though they have the DAoT Gellar Field schematics, they are not currently working on it until they have an example of an Imperial Gellar Field and understand that in full. Assuming the earliest turn around you are looking at Turn 9 for them to complete the DAoT Gellar Field research. Since they will receive the Voidship stuff on Turn 6, rolling a 1 will see it complete on turn 7 and then they will start working on the DAoT Gellar Field, which can complete the earliest at turn 8 and you get the info for turn 9.
With access to the Ad Mech, Atraxas can do the research in this case directly and as such probably faster than the Homeworld.
I believe I assumed that it was understood that DAoT stuff required an entry point to research it for the Homeworld, but I have never actually implied that. So yeah, that is entirely on me.