Its a pretty easy fault find IMO, the engineer just needs to strip everything out of the hive back plate and only run the power to it and then the switching to the boiler from it.
The black wires from the condi pump should really be connected to the boiler and not the hive but I guess if it's shutting off the HIVE, which is what calls the combi, then it's doing the job it needs to, it's just not the normal way it should be wired and it's confusing the whole thing because that wouldn't be expected.
@ianmcd will be right, the pump will probably be interrupting the power to the HIVE, which I guess is the same as interrupting the boiler but it shouldn't be on the HIVE's power, if anywhere it should be on the switching side.
Thanks goodness for pics