High-mass X-ray binaries (HMXBs) offer a unique opportunity to investigate accretion onto compact objects and the wind structure in massive stars. A key source for such studies is the bright neutron star HMXB Vela X-1 whose convenient physical and orbital parameters facilitate analyses and in particular enable studies of the wind structure in HMXBs. Here, we analyse simultaneous XMM-Newton and NuSTAR observations at ϕ_orb ≈ 0.36–0.52 and perform time-resolved spectral analysis down to the pulse period of the neutron star based on our previous NuSTAR-only results. For the first time, we are able to trace the onset of the wakes in a broad 0.5–78 keV range with a high-time resolution of ~283 s and compare our results with theoretical predictions. We observe a clear rise in the absorption column density of the stellar wind N_H,1 starting at orbital phase ~0.44, corresponding to the wake structure entering our line of sight towards the neutron star, together with local extrema throughout the observation, which are possibly associated with clumps or other structures in the wind. Periods of high absorption reveal the presence of multiple fluorescent emission lines of highly ionised species, mainly in the soft-X-ray band between 0.5 and 4 keV, indicating photoionisation of the wind.