Conventional models for predicting thermal conductivity of alloys usually assume a pure kinetic regime as alloy scattering dominates normal processes. However, some discrepancies between these models and experiments at very small alloy concentrations have been reported. In this work, we use the full first principles kinetic collective model (KCM) to calculate the thermal conductivity of Si1-xGex and InxGa1-xAs alloys. The calculated thermal conductivities match well with the experimental data for all alloy concentrations. The model shows that the collective contribution must be taken into account at very low impurity concentrations. For higher concentrations, the collective contribution is suppressed, but normal collisions have the effect of significantly reducing the kinetic contribution. The study thus shows the importance of the proper inclusion of normal processes even for alloys for accurate modeling of thermal transport. Furthermore, the phonon spectral distribution of the thermal conductivity is studied in the framework of KCM, providing insights to interpret the superdiffusive regime introduced in the truncated Lévy flight framework.