It could well be that they had medical checks/follow-ups with their doctor (= Nojiko) if the children will be fine/normal because of the inbreeding, and that they came to an agreement that the doc would adopt the kids to avoid that they would live with the social stigma, giving them a chance at a more "normal" life. They came up with a solution to get the parents out of the picture, telling the kids they died in a car accident, and there you go. They stayed away out of love for them (probably not the right call entirely though, but I guess Nojiko would also have been threatening them to reveal everything if they interfered but she will never act as it would hurt Nika and Nami). Only the civil status (= Cyrus name) gives me pause with this theory, but it is still plausible. The last obstacle is whether this canon would break Patreon ToS. I don't think it would.
I have a completely different theory. Nika and Nami are not related to Zane. They are descendants of Zoe and smone not Willy. Zoe and Nami have even more similarities than Daphne. This would explain Katie's interest and why she wants them to know the truth, but Najiko is trying to hide it. This would start a fight over the inheritance with Holgerson, who stole Zoe's inheritance after her death.
When people build theories about Zane, for some reason everyone remembers only Willie, Katie and Leah, but for some reason they forget Katerina, Scarlet and suddenly Helen. It would be funny if Nika was... not only the brother of the same Aya but also his uncle.But I personally don't think that Nika and Nami are related to Zane for many reasons. Firstly, Najiko will never be able to replace their real mother. In addition, there are a lot of questions about Naji herself. Both Nika and Nami are simply examples of upbringing, culture, etc. Especially Nami. And only 5 years later Najiko thought about a psychologist. Just think, permanent fights, antisociality, depression, etc. Mother of the year. Secondly, the lack of a father’s role has a very strong impact. No one taught him how to fight, or how to drive a car, or even how to hammer a nail. I’m already silent that he’s a walking disaster when it comes to girls. In addition, even trivially, the Zayns would have taught him martial arts from the cradle and people like Sai would be like kindergarteners for Nick now. And third. Money. Maybe they don’t starve, but they live quite poorly. Nami saved up for a bunch of months for a camera, Nika, let alone his own car, can’t even afford a license. Nadjiko works until she’s half to death. Strangers literally pay for Nika, starting from clothes to a pass to the tennis club. Seriously, would such a rich clan allow its offspring to walk around like a homeless person in cast-offs? Even theoretically, if he were a child of incest, they could hide the truth and raise him like someone found. And one more thing It seems less to me that he is Leia’s child. Firstly, Leia doesn’t care at all about the opinions of the ants. She would have raised him herself. Secondly, Leia’s descendant himself would have looked at everyone as tools. I just can’t even imagine that Leia’s descendant would babysit with someone of Victoria’s level, and even more call her or Mila friend.