The way consequences work in Diaspora hasn't changed across editions — the “3rd edition” there has the original meaning of the word “edition”, which is just a reprinting edition that contains corrections without any major changes. (In D&D vernacular, these are errata updates, not editions.) The published editions of Diaspora are all the same game, in other words. How consequences work in Diaspora editions hasn't changed, and works the same as in Spirit of the Century — aspects created in reaction to excess stress — but with the usual numerical tweaks to exactly how much of a stress hit they can mitigate, as is common among “Fate 3” games.
There are old PDFs of pre-publication Diaspora though, when it was going to be called Spirit of the Far Future and it was much more obvious (if that's possible) that it's a love letter to Traveller. The earliest I have is the December 2, 2007 revision (
SotFF-02122007.pdf) that I once pulled off a website of the designers' (which is no longer maintained, and appears to be incompletely archived by the Wayback Machine). This revision is still obviously a modification of Spirit of the Century (i.e., “Fate 3”) in not just name but also in design, and consequences in even these early drafts of Spirit of the Far Future work the same as in Spirit of the Century, again with the common tweaking.
To my knowledge there's no edition or draft of Diaspora that was based on the FATE 2.0 ruleset. When it was SotFF and I first started tracking its development, it was very much a SoC rewrite project. I'm afraid that Diaspora's development contains no pearls of wisdom about how consequences might be integrated into FATE 2.0.