I don't know what I did. I blindly followed directions for my machine (possibly failing in the following part).
I don't even know which boiler is which, though I believe the smaller boiler on my machine is indeed the steam boiler - In which case yes, the water came from that boiler.
But the instructions have you remove a sensor that is for sensing the fill level (to intentionally overfill it I presume).
I still was not prepared for a watery mess on the counter... And somehow I do not think it was supposed to happen

Edit: It is definitely the steam boiler.