Let \(\overline {M}(c)\) be a complex space form with non-zero holomorphic sectional curvature \(c\). Any (connected) real hypersurface \(M\) of \(\overline {M} (c)\) admits a naturally induced almost contact metric structure \((\varphi, \xi, \eta, g)\). Let \(A\) denote the shape operator of \(M\). The real hypersurfaces satisfying the commutativity condition \(\varphi A = A\varphi\) have been classified completely. In this paper the author proves that they all admit a naturally reductive homogeneous structure, i.e., there exists a (1,2)-tensor field \(T\) on \(M\) such that, for \(\overline {\nabla} = \nabla - T\), we have \(\overline {\nabla} R = \overline {\nabla} T = \overline {\nabla} g = 0\) and \(T_X X = 0\) for all tangent vector fields \(X\) of \(M\). Here \(\nabla\) denotes the Levi Civita connection and \(R\) the Riemannian curvature tensor. It follows that the universal covering manifold of each \(M\) in this class is a naturally reductive homogeneous space. The result of this paper generalizes a similar theorem proved by J. Berndt and the reviewer for the class of \(\eta\)-umbilical hypersurfaces.