Recent X-Point Radiator (XPR) experiments in L-mode plasmas of the WEST tokamak show that a stable radiative ring can be sustained above the X-point for approximately 70s, on timescales not limited by intrinsic plasma physics, demonstrating the compatibility of the XPR regime with long-pulse operation and its ability to mitigate divertor heat loads and tungsten contamination while maintaining core performance. Accessing this regime in future reactors, however, requires understanding its rapid formation dynamics. Here, for the first time, time-dependent fluid simulations including magnetic drifts are used to investigate the macroscopic dynamics of the rapid transition from an attached divertor to a stable XPR regime, qualitatively reproducing the experimentally observed millisecond-scale transition sequence. The simulations identify a transient X-point-centered vortex as the key transition-driving mechanism. Arising from the self-organized interplay of anomalous diffusion and drifts, the vortex regulates the entry of cold particles and impurities into the XPR region, increases neutral density and impurity concentration above the X-point without overcooling the edge, and thereby enables access to a stable XPR regime while preventing unstable XPR (known as MARFEs). By mixing cold and hot particles, steepening temperature gradients, and deepening the potential well, the vortex sustains a self-amplifying cycle over several milliseconds before saturating and decaying.