hot water tank manufacturer here…….
and the boiler now fires up when hot water requested,
your zone valve is working in that case.
(for clarity: the timer sends a signal to open the appropriate zone valve. the zone valve opens and as it reaches its fully open state, it makes a small microswitch that send a signal to the boiler (and possibly a seperate pump) to fire. this signal is sent via the cylinder thermostat – if the thermostat is satisfied, it doesnt pass on the signal to the boiler/pump.)
check:
for how long does the boiler fire once requested? if the tank is cold, the boiler should fire for 20-30 minutes at least.
what is the thermostat on the side of the cylinder set to? if it has been set too low then it will be satisied at a low temperature and turn the boiler off.
happy to chat if you PM me your phone number.