Did everything work OK before you installed the Hive? If so, then it will be something you have done wrong when transferring the wires over from the EP to the Hive. If you start altering things that you haven't touched in the process already, you can run the risk of introducing more problems.
The EP contained two internal switches. On/off for hot water and on/off for central heating. The Hive is exactly the same, it contains the same two switches, so electrically speaking nothing should have changed (except for the bypassing of the old room thermostat).
The pump is not normally connected to the programmer. Usually it is controlled either from the motorised valve, or the boiler depending on the set up you have.
If the pump is wired to the motorised valve/s, then in operation, the motorised valve winds opens the central heating outlet which also triggers an internal switch that is responsible for starting the boiler and pump. However, your valve isn't opening but the pump is running, suggests to me that it's possible that the pump wiring was connected to the EP spare terminals and now somehow you have connected it to the heating on connection at the Hive, and maybe the motorised valve is now connected to where the pump should be. All you can do is trace the wires back and check, it's not possible to be more specific over a forum without being physically present to inspect the wiring.
The Hive 'heating on' terminal (4) normally would go (via the now joined original thermostat wires) to the motorised valve's heating live wire (white wire if it's a 3 port valve / brown wire if it's a 2 port valve). That of course doesn't take into account the "strange accoutrements" which will be connected in somewhere.