We will consider single transverse spin asymmetries in the inclusive particle production within the framework of the generalized parton model (GPM). By carefully analyzing the initial- and final-state interactions, we include the process-dependence of the Sivers functions into the GPM formalism. Within this formalism, we make predictions for single inclusive pion and direct photon production at RHIC energies. Also we consider the azimuthal distribution of leading pions inside a fragmenting jet as well as single inclusive jet asymmetry in polarized proton-proton collisions. In contrast to single inclusive pion production, we can isolate the Sivers contribution and thereby study its process dependence. However, in all cases, we find the predictions are comparable in size but opposite to those in the conventional GPM approach. We conclude that these processes represent unique opportunities to discriminate among the two approaches and test the universality properties of the Sivers function in hadronic scattering reactions.