If there is any kind of rough physics to it, the first blast is the star 'breathing off' its outer layers, and the second is the core of the star collapsing.
From my understanding of physics a supernova is a single-stage explosion caused when the star collapses in on itself enough that it reiginites considerably more intense fusion, essentially blowing it apart as its gravity is no longer able to control the reaction. (Though to be honest in basic computer simulations of it what appears to happen is the star's exterior layers collapse back, hit the core, and bounce, amusingly enough.) Losing its outer atmosphere, which isn't even necessarily a stage, should have been a considerably more...gentle
result then what we saw. We know that most FS ships can stand up to starlike temperatures for brief periods, and the exterior atmosphere sloughing off would have been a brief pulse of that kind of heat, with almost no pressure component. Anything that could absorb a Helios hit or two would have been able to handle it, but this did considerably more damage.
As Capella was apparently a normal main-sequence star lacking the mass to go supernova, it would be my guess that that we saw toast the Moloch and Deimos was, in fact, the Capella supernova. We know FS ships are ridiculously durable and able to withstand things that our current materials science says are completely impossible to resist.
However, given that the most likely method the Shivans had of triggering such a supernova was to interrupt the flow of energy from the star's core to its surface via subspace portals, I think that what came next was essentially subspace fighting back; dumping that much energy into a node would have definitely collapsed it, after all. The Shivans opened, and held open, portals in the face of an energy input that makes the detonation of the Lucifer or Bastion pale in comparison. When they stopped, the resulting subspace cataclysm was certain to be impressive...perhaps impressive enough to breach the boundaries with real space.