Charge-density waves (CDWs) in kagome superconductors are a key ingredient for understanding how electronic order interacts with superconductivity. In this work, we study how the CDW evolves under pressure in the kagome metal RbV₃Sb₅ using temperature-dependent in situ EXAFS. We observe that the CDW is closely linked to local lattice distortions, which become weaker and shift to lower temperatures as pressure increases, consistent with the suppression of CDW order. A closer inspection of the local structure reveals a distinct pressure-dependent behavior. For pressures below 0.9 GPa, we observe a reduction in the in-plane Sb-V distance within the kagome layers. This structural change occurs at the same temperature as the CDW onset and follows its suppression, decreasing as pressure is applied. For pressures exceeding 0.9 GPa, a second local distortion emerges, manifested by a change in the out-of-plane V-Sb distance. These results indicate that the CDW state undergoes a fundamental modification, suggesting a possible change in the CDW order. This structural evolution follows the superconducting phase diagram and may be related to the double-dome behavior observed in this system. Therefore, a continued investigation of the local structure is essential to further elucidate the complex correlations between these lattice modifications and the emergence of CDW and superconductivity in these kagome-based systems.