As another side note regarding the Dyson: the gatlings that have been spawned seem to only patrol my planets; they don't ever venture into enemy territory. Is this intentional? I think this --- i.e., allied factions never going on offense --- has been complained about before, but I don't recall the resolution.
Once you start going on a significant offensive endeavor OR when there is a substantial threat build up, then they will go out and start attacking.
A word of caution though, Dyson gatlings, for whatever reason, are very slow to notice a "significant offensive endeavor", and it will probably take quite some time before they start helping your attack out. Quite likely, they won't notice it before you finish your attack, and thus not help out at all.