Context. Radio galaxies classified as X-shaped/winged, are characterised by two pairs of extended and misaligned lobes, which suggest a rapid realignment of the jet axis, for which a potential cause (including binary supermassive black holes, a black hole merger, or a Lense-Thirring precession) is still under debate. Aims. Here we analyse the complex radio structure of 3C 293 winged source hosted by the post-merger galaxy UGC 8782, which uniquely displays a significant asymmetry between the sizes (and therefore the ages) of the two pairs of lobes, indicating that an episode of jet realignment took place only very recently. This allows us to tightly constrain the corresponding timescales, and therefore to discriminate between different models proposed for the formation of X-shaped radio galaxies in general. Methods. Based on all the available and carefully re-analysed radio data for 3C 293, we have performed a detailed spectral modelling for the older and younger lobes in the system, using the existing evolutionary DYNAGE algorithm. In this way we derived the lobes’ ages and jet energetics, which we then compared to the accretion power in the source. Results. We found that the 200 kpc-scale outer lobes of 3C 293 are ~ 60 Myr old and, until very recently, have been supplied with fresh electrons and magnetic field by the jets, i.e., jet activity related to the formation of the outer lobes ceased within the last Myr. Meanwhile, the inner 4 kpc-scale lobes, tilted by ~ 40° with respect to the outer ones, are only about ~ 0.3 Myr old. Interestingly, the best model fits also return identical values of the jet power supplying the outer and the inner structures. This power, moreover, is of the order of the maximum kinetic luminosity of a Blandford-Znajek jet for a given black hole mass and accretion rate, but only in the case of relatively low values of a black hole spin, a ~ 0.2. Conclusions. The derived jet energetics and timescales, along with the presence of two optical nuclei in UGC 8782, all provide a strong support to the Lense-Thirring precession model in which the supermassive black hole spin, and therefore the jet axis, flips rapidly owing to the interactions with the tilted accretion disk in a new tidal interaction episode of the merging process. We further speculate that, in general, X-shape radio morphology forms in post-merger systems that are rich in cold molecular gas, and only host slowly spinning supermassive black holes.