  Each hypersurface of a nearly K\"ahler manifold is naturally equipped with
two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the
induced almost contact structure $\phi$. In this paper, we show that, in the
homogeneous NK $\mathbb{S}^6$ a hypersurface satisfies the condition
$A\phi+\phi A=0$ if and only if it is totally geodesic; moreover, similar as
for the non-flat complex space forms, the homogeneous nearly K\"ahler manifold
$\mathbb{S}^3\times\mathbb{S}^3$ does not admit a hypersurface that satisfies
the condition $A\phi+\phi A=0$.
