Having done a few solo jumps myself...this seems really wrong.
Tandem jumps usually have a drogue to slow everything down. Then there's the main chute, which I believe in tandems is deployed with a pilot chute, NOT by a spring. The pilot chute drags out the main chute.
If something is wrong - such as the main chute not deploying or having a line over, then you can pull the reserve chute. When you deploy the reserve parachute, there are two stages to it: the first one is the RSL - the act of pulling the reserve handle cuts the main chute lose by releasing its risers, and as the main parachute is let loose it drags the reserve out. The second stage when you're pulling the reserve handle ALSO deploys the reserve chute, which is spring loaded essentially (in the case that the RSL fails, was disengaged or you never had a main out in the first place - reserves deploy faster than mains, so you can end up in a situation where you never got your main out but still ended up under your reserve.)
Finally, should ALL else fail, you have a cypress device on you. You zero it on the ground (at the drop zone). When you're in free fall, the device typically arms at 1000 feet. If at 800 feet you're travelling >28mph downwards, it deploys the reserve automatically (though it does NOT cut the main away, so you can end up in some strange configurations with a biplane setup going for example.) These devices are meant to handle situations such as a jumper being unconscious during free fall...or someone just not paying attention to their altimeter.
Long story short....I don't see how this would have happened. A lot would have had to go wrong for them to not deploy a main, not deploy a reserve and then for the cypress to not fire the reserve on its own.
I can ask my father in law...he's got a couple thousand jumps and has had to write a few of fatality reports over the years...he may know more about what happened here.