Usually, off-peak immersion cylinders have two heating elements. One can only come on during specified cheap rate times. The other can be switched at any time, but will incur the full rate. It sounds like you have this arrangement.
But ............ it depends entirely on which metering system you have. One of the systems has a "two-rate meter". This means the whole house goes over to cheap rate during specified times. This means that you don't have a separate meter with dedicated off-peak times. Very handy for running washing machines and the like overnight at reduced rate.