The quantum transition state framework was developed to calculate the reaction path-resolved scattering matrix for atom-diatom reactions in hyperspherical (APH) coordinates. This approach allows for simply and directly calculating the reaction path-resolved scattering matrix, especially when the encircling reaction path is negligible. It could be used to determine the reactivities of specific pathways in a chemical reaction, providing insights into phenomena such as geometric phase effects. To validate our method, detailed calculations for the H + H2 reaction at J = 0, 1, 2 were carried out, and the results were compared with those from our previous theoretical models including the geometric phase effects. Analysis of the path-resolved reaction probabilities reveals that encircling paths play a very minor role in this reaction, even at energies exceeding the conical intersection minimum. Furthermore, the analysis suggests that the geometric phase effects arising from the interferences between different reactive pathways could become more significant for highly rotationally excited reactants and products.