In this work we explore the applicability of the adiabatic rotation approximations to state-to-state quantum reactive scattering for three-body systems within the context of the coupled-channel hyperspherical coordinates method. A novel refinement to the adiabatic rotation approximation advocated by Bowman (Chem. Phys. Lett. 1994, 217, 36) has been obtained by the inclusion of the asymmetric rotational terms into the Hamiltonian. Within this approach, the total Hamiltonian is separated in an exact Hamiltonian for zero total angular momentum plus an effective rotational energy term that is added to the potential energy surface to form an effective potential on which the reactive dynamics evolves. Calculations of state-to-state reaction probabilities, integral and differential cross-sections for the prototypical reactions Cl+H₂ and F+H₂ are presented to test their accuracy and computational advantages in comparison with exact quantum mechanical calculations.