The answer to the question is that the second, i.e. existing pressure vessel does cause a problem with certain settings on mixer taps as follows:
As mentioned above the HW tank is pressurised, whereas the cold water pressure is provided once the pump starts, the water will flow under gravity if the configuration allows it.
The effect of the second pressure vessel is that the hot water will flow on its own for longer, with the result that not sufficient cold is being delivered to the mixer tap if the cold is not opened sufficiently.