Partially correct but they are also partly to blame for the mess.
The meter is a 5 wire type, the 5th wire would be the switched output for the night storage heaters. Nothing is connected to the 5th wire output (black plug on the underside of the meter between the wires marked 3 and 4).
For it to be used correctly, an additional wire is required from there to the other switchfuse in the cabinet to the left - the top one is connected and is the 'day' circuits in your new consumer unit, the lower one would have been connected via that 5th meter wire to the other old fusebox for the night storage only.
You also need another consumer unit, or the existing one modified, so that the switched 'night' input is connected to the storage heaters.
Therefore the meter installer should have connected that 5th wire
and the electrician should not have shoved the storage heaters all onto a single circuit in the same consumer unit
Not related to your problems - but the whole arrangement of those meters and the old switchfuses is in desperate need of a major overhaul and has been for several decades.