"Explosions are caused by the release of high pressure Gases-Either through Combustion or release of Pressurized Gas". Your quote, and it fits well the circumstances as evidenced by the images and statements?
Bear, the posters are correct to point out the engine did not "explode" in the classic "release of high pressure gas" way.
The failure of the disc will be down it exceeding its mechanical properties due to centrifugal/petal (i.e. spinning) forces. As stated, this is likely to be either due to overspeed or heat damage to the disk material.
To illustrate - imagine spinning a 1kg weight around with your arm on a piece of thin string at 1 rev per second. You can imagine that if you tried to spin it at 3 revs per second, the string might break as the forces needed to keep the 1kg weight spinning are higher than the strength of the string. This basically the same as the IP disc - the forces at 7000rpm (or whatever it spins at) are huge, and the disc is designed to be strong enough for "normal" spin speeds only, with some margin. If it was designed to survive e.g. 20,000rpm it would end up being far too heavy - so it isn't, and an overspeed will lead to the 'string breaking' in the IP disk.
Secondly, the disc material is key to its strength - hence if you were to set fire to the string even with the 1kg spinning at 1 rev per second, you can see that it would weaken to the point where it would break even under a normal 1rev/s speed. Obviously a metal disc doesn't burn under fire like a piece of string, but its mechnical strength can still be significantly changed - even at modest temps well under melting point to the point where it is no longer strong enough to spin at its normal speed of say 7000rpm.
Hence, there is no classic gas explosion, it is a material failure of the metal that leads to the exit of the disk in various pieces.
One final thought - this is speculation only, no evidence - it maybe that the first "bang" was the turbine/compressor becoming "disconnected". This would allow to turbine to rapidly accelerate (i.e. no longer working to turn the compressor so can spin as fast as it likes) and overspeed - hence burst and create the second "bang" soon after the first. Overspeed wouldn't take long to be achieved after initial "decoupling".