Here is some 'out loud' thinking of mine on the problem with your installation.
How the CH sub-system is meant to work. If the programmer 'allows' CH to run (ie: ON, advance, timed on), then if the room stat is closed on under set-temp, a signal is sent to the ASHP to 'Go CH'. The ASHP responds by sending a signal out to the 2PMC(CH) which opens. When the 2PMV(CH) has opened, its internal auxiliary switch closes which sends energisation to the water pump. ALL THIS HAPPENS. Note no signal generated yet to run the ASHP.
To begin with the circulating water through the CH circuit is warmed by the Buffer Tank Direct(BTD). The temperature of the BTD is monitored its own tank stat. When its volume of water has cooled such that it no longer can warm the water for the CH circuit, the stat closes and sends a signal to the ASHP to run - THIS DOES NOT HAPPEN. Once the radiators have warmed the room the room stat opens. This does not immediately stop the ASHP because the ASHP has further work to do to reheat the BTD. So this means the 'Go CH' signal is latched in the ASHP and only unlatched once the BTD's stat opens. If Go CH was not latched then ASHP would stop immediately preventing BTD from being reheated. In the logic state of (no space heating required and BTD heating required) the ASHP sends a signal to divert water flow to the spring loaded 3 port valve - valve 3 on page 22 of manual reference. BTD heats up until its state opens: then ASHP shuts down. There is now a ASHP next start delay initiated circa 3 minutes.
If there has been a HW demand, I think it too is latched and only cleared after the HW tank has been heated to temp and the BTD reheated too. This might explain why radiators are being warmed after there has been a HW demand.
So why no operation of the CH sub-system independently of the HW sub-system? When I did a test which removed the priority to HW which is set in the ASHP, - 2PMV(CH) opened and the water pump ran. Nothing else. This indicates that the signal from the BTD is not being generated. Examining the wiring diagram on page 22 of manual reference the source of 230V for this signal is taken from the output of the HW stat (on page 22 upper terminal block - terminal 21 is linked to 18 and 12). This creates the logic that a BTD heat demand from its stat to the ASHP to run can only be generated if HW stat closed(HW GO to ASHP). I suppose during the test the HW tank was at temp so no HW GO which would explain why ASHP did not start.
So if I am on the right lines the installers have followed faithfully the wiring diagram with an error as described on page 22 it would explain why the installation has a problem.
I have a query into Ideal Boilers because I reckon the wiring diagram page 22 has an error. The BTD stat line input should be taken from terminal 14 the input to the room stat.