A sees that the calcium clock of B runs slower, and viceverza. But the problem is not symmetric. First, the supernova is moving relative to one of the observers. That observer will see that the distance betweem him and the supernova is smaller than what the stationary observer will see. Second, at least one of the observers has to accelerate if they are going to meet again. The acceleration changes things in such a way that the cesium clock has marked less ticks for the moving/accelerating observer. To him, the cesium clock of the stationary observer was running slow when he moved at constant speed, and then accelerated when he was decelerating.
Case with no acceleration: Asumming that the star explodes when the distances to both is the same according to A, then A will see that B marks a larger time than him. Even if to him B's clock is running slower, he see that B marks the explosion after it happens. To A both events, the explosion and B writing the time of the explosion, are not simultaneous.
B will also see A's clock as running slower than him, and will also see that the explosion happens before A marks the time. But to B the explosion happens when the star is closer to A than to him.