Most utilities don't yet have the ability to do time-of-use billing for their residential customers, so this billing scheme won't be widespread until smartmeter deployments see more progress.
And yes, nighttime electricity is cheaper due to the types of plants used to produce it.
Baseload power is power produced by cheap, inflexible generation sources such as coal, nuclear, and hydro. Their fuel sources are inexpensive, but they can't easily adapt to demand. They produce at 100% round-the-clock.
Intermediate load sources can scale their energy output up and down throughout the day according to demand, but use more expensive fuel than baseload plants. Example would be gas-turbine power plants fed with natural gas or landfill gas.
Peaking plants can quickly provide demand response for the highest use scenario. They're the most expensive to operate, with fuel sources such as oil.
So, utilities and RTOs (regional transmission operators, the entities that control regional grid stability) in deregulated markets spend a lot of effort making sure that peak capacity is there for afternoon loads on hot summer days. Conversely, power at night is cheap, to the point that generators are sometimes paid to stop feeding power onto the grid.
Hence the availability of free nighttime energy in markets with the metering infrastructure to support it.