that there is, in fact, no pressure spike. The pressure of the sealed chamber decreases due to the rupture, lowering the transition temperature of the supercritical fluid. Some amount of that fluid will then vapourize and distribute the pressure over the much larger volume of the two-chamber system. Increasing the total system pressure still requires external input.
Much like any other explosion, a BLEVE occurs when very fast moving objects in close proximity all suddenly have somewhere to go. It does not increase the pressure of the system it is in.