Site-specific Seismic Probabilistic Tsunami Hazard Analysis (SPTHA) is computationally demanding, as it requires in principle a huge number of high-resolution numerical simulations for producing probabilistic inundation maps. We implemented an efficient and robust methodology that, based on the similarity of offshore tsunamis and hazard curves in front of a target site, uses a filtering procedure to reduce the number of numerical simulations needed, while still allowing full treatment of aleatory and epistemic uncertainty. Moreover, near-field sources are identified, on the basis of the tsunami coseismic initial conditions, and treated separately to avoid biases in the tsunami hazard assessment. In fact, coastal coseismic deformation necessarily affects the tsunami intensity, depending on the scenario size, mechanism, and position. Therefore, we developed two parallel filtering schemes in the far- and the near-field, respectively. For near-field sources, offshore tsunami amplitude can not represent a proxy for the coastal inundation, and filtering is based on coseismic field. By comparison of the results obtained with and without the correction for the near-field sources, for a use-case at the Milazzo oil refinery (Sicily, Italy), we demonstrated that special treatment of local sources plays a fundamental role and is applicable in local scale SPTHA.