With the sort of figures you're talking about (which I suspect are probably reasonably 'typical'), it is difficult to see how (certainly in Winter), even the entire solar generation (let alone 'excess' generation) would presumably never be enough to power a standard 3kW immersion (for any period of time), would it (given that immersion heaters are entirely dumb passive loads)?
yes, that's right.
but
the immersion controllers only send power when there is excess power generated, above that used in the house (which they detect by measuring exported power on the meter tails)
and they reduce the voltage to the immersion so that (since it is a simple resistive load) it does not use enough to reduce exported power to zero or below. AFAIK they work like a lighting dimmer that clips the peaks, and the amount of clipping is controlled by the exported power it can measure on the meter tails. It has a sort of clamp meter, I don't know how it manages to detect direction of flow.
so, if you have 500w of exported power, they will divert (about 450W) to the immersion
although, on dull winter days, exported power may be zero most of the time. There may be a bit when the sun pops out from behind a cloud if, at that moment, you are not using a kettle, toaster, washing machine etc
The money-saving figures quoted in the ads seem to be based on the assumption that you live in an all-electric house. Cost of HW by gas is tiny and savings do not make these controllers an economic proposition.
If however you live in an all-electric house, you don't need a controller, you may as well just have a timer to run the immersion from 10am to 4pm, in which case it will pick up whatever solar power there happens to be, and you have to heat the water electrically because you have no other option.