Undercooked eggs that were in the pot plenty long
If your eggs came out soft boiled then that means they weren't exposed to enough heat - something in your method went wrong. I suspect that when you turned it down low the water temperature dropped below 140-150 degrees F, which is the temperature that egg white will cook. It doesn't matter how long you cook eggs below 140F, they will never get done below that temperature. 

To fully cook egg white it must be heated to 150F, egg yolk to 160F. If your eggs were cold when you put them in and the water boiled quickly the inside of the egg would still be fridge temperature, so when you turned the heat down low the eggs cooled the water below 140F, and the amount of heat the burner was producing wasn't enough to heat the water and eggs above 140-150F.

I use a similar method, however I put a lid on the pot which makes a big difference. If you don't want or have the right lid simply keep the heat turned up to where the eggs bounce around a bit.