Aluminum electrolytic capacitors are polar specific, so my best guess is that (as @CaptDon mentioned) the capacitor that exploded was likely wired to the board backwards. All I found on the floor afterwards was the aluminum capacitor cover.
Indeed it was cheap Chinese junk. I paid $6.99 for it on Amazon. It had zero reviews. I just left one explaining that it exploded. I would have given it zero stars, but one star was as low as I could go. The Amazon reply was that it will take several days of review before my response gets posted for public consumption. I'm betting it won't be posted at all.
Fortunately I was off scrounging for my tiny potentiometer screwdriver when it went bang, as I could have been injured.