Double-core-hole (DCH) states offer a unique window into electron correlation and multi-electron dynamics. Using intense x-ray free-electron laser (XFEL) pulses and high photon-energy resolution, we generate DCH states in neon via sequential absorption of two x-ray photons within the 1s core-hole lifetime (=∼ 2.4 fs). These DCH states are populated, depending on the photon energy, via two different pathways, and they are detected via their KLL hypersatellite Auger decay. A high-photon-energy-resolution study of these two pathways, previously identified in water, allows us to reveal further details of the corresponding processes. The sequential double-ionization with two photons also allows us to study post-collision interaction (PCI) in a four-particle system consisting of the remaining ion, as well as two photoelectrons and one Auger electron, each with well-defined velocities. The observed PCI shift is well described by a theoretical approach based on the eikonal approximation and shows that the influence on the Auger electron is dominated by the slow photoelectron, while the fast photoelectron provides only a minor correction. Calculations show that for the utilized two-photon double-ionization scheme to prepare DCH states, the length of the FEL pulse influences the PCI shift.