already said this but you need to set the HW to constantly on, the new stat will control the CH pump as long as the store is satisfied
I am certain this is not the case - I am sure of this because this is not set to constantly on with the set-up I did with Nest and is working fine now, and the hot water can be timed exactly the same as before. If you just replace the thermostat wires then it could be any thermostat connecting to the boiler, it’s still just switching live when it wants heating.
Maybe you do it differently.