Tube-fin heat exchangers, as a form of compact heat exchanger, are widely used in the refrigeration industry. The contact state affects the heat transfer efficiency and contact thermal resistance, which are crucial indicators for evaluating the heat exchange performance of heat exchangers. In the manufacturing process of tube-fin heat exchangers, the fins undergo elastic-plastic deformation and springback, after which the heat exchange tube is pressed to achieve an interference fit and establish contact. The variation in the springback after the plastic deformation of the heat exchange tubes and fins is the direct cause of their contact. Therefore, there must be a certain relationship between springback and contact. In this study, the assembly connection of seamless internally threaded copper tubes is investigated with a diameter of 7 mm and aluminum foil fins using hydraulic expansion technology. The effects of the expansion pressure on springback and contact were investigated using experimental methods and finite element simulations. In this study, the springback behaviors of copper tubes and fin flanges during hydraulic expansion were investigated, and data-fitting methods were used to elucidate the relationship between springback and contact. The results indicated that within the expansion pressure range of 13–17 MPa, the average springback of the copper tube and fin flange increased linearly with the expansion pressure, whereas the springback rate decreased inversely. The difference in springback between the two is exponentially related to the contact gap.