The questions this raises are:
Is your drain line plumbed to your steam room or to a drain near the steam generator.
The water solenoid is allowing what to enter but not stop because the water probe is not getting a signal that the tank is full. This would not be a heating element issues.
If the drain pipe is not piped into the steam line to discharge in you shower, then I would look to the water probe that is not getting satisfied on water so it cause your tank to overfill and the only place the extra water can escape is through the steam line.