> hrow water on the rocks?

Depends on the location! Very often, at public locations there is a "saua master" taking care, in smaller locations I have seen people handling this on their own.

And in one location there was a sign: "no private watering due to electrical issues"

I think I've heard US it's mostly no water at all on stove and Germany I've heard they have had these sauna-masters who come and cast water on stove.

Neither of these are practised anywhere in Finland at least. But there are at least one Finnish swimming bath where they had to limit steam competitions and made a button controlled mechanism to administer water instead of free usage. Not because electrical shock prevention but because bad human behaviour per se.