As you still haven't confirmed the type of system you have, (i.e. Y-Plan / S-Plan / Gravity hot water with pumped central heating / something else?) but you don't mention any motorised valve/s, I suspect that you may have an old system whereby the hot water is heated by natural gravity circulation (warm water rises, cooler water falls) so that whenever the boiler is 'on' hot water from it circulates around the hot water cylinder. Then, when the heating is required, the pump is turned 'on' by the room thermostat and circulates water from the boiler around the radiators. Something like this:
Based on that, if you do have this sort of system, I think that you may have a problem in the summer. If the boiler was controlled by the TimeGuard so that whenever it was 'on' you got hot water, and the heating could be turned off by the room thermostat. [at least that's how it should have been wired for this type of system] The situation is now different. Hive takes over the functions of both the TimeGuard and the room thermostat in the same unit, providing only one output, so you may find that in the summer it will be necessary to have the radiators actually hot, in order to get the hot water cylinder heated as well. The pump doesn't seem to feature in your wiring diagrams so without knowing where it's connected into the circuit, it's impossible to tell, but to avoid this scenario the pump should not just be wired to the same LN&E as the boiler.*
The usual arrangement for the wiring of a gravity hot water pumped heating system to a dual channel Hive is:
Here, when the hot water only is 'on' the boiler fires up and the hot water circulates around the hot water cylinder. [The pump doesn't run so the radiators remain cold] This allows the hot water only to be heated in the summer.
When heating is required the pump is started and circulates water around the radiators. However the boiler obviously also has to be on, so the hot water would still need to operate. Hive has a function that allows this to happen automatically. But the wiring would need to conform to my diagram above for it to work.
*The final fly in the ointment, is that if your boiler requires a pump overrun, (i.e. it's controlled by dedicated pump terminals from the boiler) then it can't be done, and your boiler is not suitable for this type of system. This would then of course explain the lash up of the existing wiring to try and get around it and as it originally was you wouldn't have been able to heat just the hot water cylinder without having the radiators on as well.