In a recent paper [10] we introduced the notion of Levi harmonic map f from an almost contact semi-Riemannian manifold (M, ${varphi}$, ${xi}$, ${eta}$, g) into a semi-Riemannian manifold $M^{prime}$. In particular, we compute the tension field ${ au}_H(f)$ for a CR map f between two almost contact semi-Riemannian manifolds satisfying the so-called ${varphi}$-condition, where $H=Ker({eta})$ is the Levi distribution. In the present paper we show that the condition (A) of Rawnsley [17] is related to the ${varphi}$-condition. Then, we compute the tension field ${ au}_H(f)$ for a CR map between two arbitrary almost contact semi-Riemannian manifolds, and we study the concept of Levi pluriharmonicity. Moreover, we study the harmonicity on quasicosymplectic manifolds.