There's quite a lot of info in that attachment but some, like the output logic, a bit confusing, to me, at any rate.
The cylinder shows two probes (quite normal), one, the "Low" is installed just above the solar heating coil, the other, "Aux" is installed (normally) in the cylinder top with the boiler coil below it may be heating maybe the upper two thirds of the cylinder so you could have the upper two thirds at 70C but the lower as low as 15C or so, the solar system should then heat this one third up as well, OR if no boiler on, the solar will heat the whole cylinder.
The pump shows a start contact L1 but doesn't show what energises this as the logic shows this switched only for controller models 501 & 501D, (yours is 502D), what it does show though is that the pump stop contact L2 is energised when "T.high < T.low+T.diff which means when the solar panel temperature is (or falls) to the store temperature+4C then the pump stops, this means, by inference, that once the solar panel temperature reaches store temperature + 4C + the hysteresis (given as 1C), ie, when the panel temperature increases to store temp + 5C then the L2 is de energised and the contacts will switch over to L1 and pump restart. If this is how it operates then very unusual IMO to use a normally closed (NC) contact and a set switching hysteresis of 1C but it is what it is, maybe?. I would also increase that 50C SP to say 65C.
Its a mystery though why the circ pump runs for hours on end as we can see now that its not variable speed controlled, the schematic also shows a motorised valve, don't know what this does. Your cylinder should heat up in a few hours in this weather using solar only, mine is reaching 65/70C every day for the past 4 or 5 days.