These mutations lay on the Z chromosome. Male birds have ZZ and females have ZX. For a sex-linked mutation to be visual, it must be on all of the Z chromosomes. That means that females only need to get one gene of the mutation in order for it to be visual. Because of this, females cannot be split to sex-linked mutations.

So if a male bird is split to one of the sex-linked mutations, and the female doesn't carry it at all, only half of the females will be the mutation and half of the males will be split to it.

If a male is visual and the female is not, all of the female babies will be visual and all of the male babies will be split.

If the female is visual and the male is not and not split, all of the males will be split and there will be no visuals.

If the female is visual and the male is split, all males will carry at least one of the genes (so some will be visual) and females will either be visual or not carry it at all.

If both parents are visual, all babies will be visual.

If the baby is a sex-linked mutation and no parent is visual, it means the dad carries it and the baby is a female.

In the case of Lutino and Australian Cinnamon:
When a male is split to both Australian Cinnamon and Lutino, it looks like an Australian Cinnamon. The mutation is called SplitCinnamino or SplitPallidino.