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What correlates the x-ray flash to the precise rate of rotation of the pulsar is that the flash emanates from a thermonuclear explosion that is understood to occur on the surface of the pulsar, in a fixed spot on the ground, not in space near the pulsar or in it's "atmosphere". It's just like a spotlight on Earth, in a sense. As for the rotation of the pulsar varying, it has long been known that they slow down over time, infinitesimally to be sure, but never the less they do wind down due to friction with surrounding gasses, as well as from gravitational effects. Measurement of the Crab pulsar, the first ever discovered, has proven this.