I new damn well that I should have kept away from this!
ALL of these types of water pressure systems have to have an "air cushion" that provides the pressure. You cannot compress water, so the pump shifts a volume of water into the holding tank against a certain volume of air, which is compressed and builds up pressure. As in ANY enclosed system the total pressure in the system is reflected on to all parts of that system, it is basic physics. The pressure switch is connected so that it senses this pressure, and is set to stop the pump. When you draw water off the system the pressure will start to drop until what is termed the "differential pressure" setting is reached, whereby the pump is switched on again and the cycle repeated.
In earlier, and probably some current bigger systems, the holding tank was fitted with a rubber "bladder". The water is stored on one side of the bladder and the air on the other side. BUT, the big difference with this type of system is that the airside has to be pre-charged and maintained to a given air pressure. They are more reliable and maintain pressure more accurately and usually have a bigger reservoir tank that allows for a bigger drawdown before the pump has to run again. Apart from that they work on the same principle as your system.
With the small types of pumps used here, and many other places, there is no "bladder" to separate the water and the air. From being empty of water to start with and only atmospheric air pressure, the pump moves water into the tank and starts to compress the air. It will continue to do that until such time the total pressure reaches the pressure switch set point and the pump stops. Draw off some water and the pressure drops below the differential setting and the cycle repeats.
The point here is that the reservoir tank HAS to have a space for air. That is why I suggested that you drain the tank and start again. HOWEVER, I also posted that these pumps are called "shallow well pumps", which means that they are NOT designed to have a "flooded" suction head from a surface tank. The constant head of water from your surface tank can allow the water to flow through the pump and "flood" the reservoir tank, eventually resulting in no air space to build up pressure. I have found that Mitsubishi pumps do not have this problem, but I am not sure about Hitachi, but as the problem appears to have coincided with the replacement of the pump, it is more than likely they are susceptible to this problem.
The drain plug I referred to may be hidden under the plastic stand the unit sits on so it is not obvious.
You have posted that the pump is a "constant pressure" pump. I have not seen them here but then I am no longer directly involved with the things. I will post a link to a site that shows the difference. On both of the examples shown you should note the air space in the reservoir tank, albeit one of them is shown inverted.