It works the same as a car thermostat. If working properly it keeps the outlet temperature the same no matter how hot the inlet temp is. So if the cylinder is not very hot. It simply passes the cylinder temp to the outlet. Surprised the plumber didn't replace it. It is common for them to fail. But often they will jam on full hot and the customer doesn't notice they have 60deg water to their taps instead of 55deg.

At least one tempering valve manufacturer recommends that their valves be replaced every 5 years. So that is why I just normally replace them. I'm a plumber myself.