The layers, upon layers, to them coming together as a team!
The first time Bren runs back for one of his bodyguard, he gets slugged for it. By his bodyguard! Because he's not their lord, he's their principal; he's their job as an object, not a subject. (The subject is Tabini.) And he's done something utterly stupid and wrong to the atevi mind: he has jumped in a direction .
But by the time we get to the first space trilogy, Bren has accrued not only a household full of atevi who ... cannot officially say they feel man'chi toward him, but also a team of four Guild Assassins of high skill assigned to him who also ... cannot officially say they feel man'chi toward him. And this not-technically-an-aishid has been acting, for the entire first trilogy, like Bren is an object and not a subject. They work for Tabini, they are not an aishid, they are emphatically not Bren's aishid, except they are, because what else could they be?
But on their own planet, on their own continent, in their own culture, those barriers are solid. In space, on a human starship, on a human space station, with their own island of atevi sanity precariously constructed adjacent to the Dowager's, and Tabini two years away, the walls come down. The shapes they are in, as household, as aishid, anchored on Bren—what if they stopped pretending it was pretense? What if they let it be real?
What if, Jago says, we let Bren really play the part of our liege lord? Then we can stop playing parts, and our instincts will just work. The one thing that's missing, the one thing that's not "real" about their arrangement, is Bren as object. And Bren has never, to this point, really slotted in neatly that way. The shapes of atevi life around him don't precisely work if he isn't their active, agentic subject. There's an atevi intimacy to the aishid wrapping itself around their lord, a gut-level rightness, that's being held at a distance as Banichi and Jago keep treating their job as in some sense still working for Tabini, part of which is guarding the human, part not. Sure, they're going to have to deal with the fact that their lord has a tendency to try to protect them—but that has its own benefits, and out here in space, surrounded by humans, making up so much as they go along, can you imagine the temptation as they give in to it?
And when they return home, to the other half of the aishid, left behind, to the bulk of the household, left behind, to the office staff, for that matter, left behind, all left still reaching for the anchor displaced two years away in space, not in fact having gone off to other man'chi, or returned neatly to Tabini? Everyone is going to take their lead, not least because in chaos that is the most basic atevi instinct. Especially because attaching themselves to Bren for real, as Bren and the Dowager and Cajeiri together set the world back on its axis, as Tabini returns, as the whole complex, massive structure of man'chi returns and is affirmed, proves itself right because Bren proves himself part of it all.