Maybe Akali's mother knew the shadowy techniques and helped to seal them away. She passed them to her daughter so that one day someone would understand the way of the shadow should it ever need to be defeated.

From what I have seen, Zed "continued" the order by telling Akali that she needs to kill for the Kinkou like her mother. Since both were Fists of Shadow. They did it without question and often many of Zed's targets were on the weak and innocent (given how his passive is "Contempt for the Weak"), claiming the weak disturbs the balance of nature.

It was only when Shen performed the Stand United move did she learned about Zed's deception and she joins them or face judgement at the hands of him.

They were luvers!!!

The Fist of Shadow was a part of the Kinkou order before Zed's arrival, so that must be taken into account. It is possible, as I see it, that Zed's powers come from the same place Akali's do; that box. It would tie in nicely with the idea of balance Ionia presents:

Shen is an Ionian who very clearly walks between Light and Dark.
Kennan is the member of the Kinkou that is heavily invested in the Light side.
Akali, therefore, must fill out the latter end of his spectrum: becoming the Dark side and gaining her power from some kind of similar source.

This theory, of course, does not rule out the potential they are related in any way (be it by blood or mentorship) and I would also love to see that kind of potential played out in character development.