Can a vacuum in a room increase the pressure in a tube?

Ok, So I work as a Marine Engineer but I do not have an engineering degree so I am having a hard time wrapping my head around this problem.

So currently on my ship we had a minor spill overboard from our black water collection tank (lower left) where air was drawn in from our grey water (lower right) tank. The air that was drawn in agitated whatever liquid was in the black water tank, causing it to foam and go overboard.

Background Information

The grey water tank is in a machinery space that is very well sealed in case of a fire, lets make the assumption that it is a sealed box. The water from our sinks, showers and drains gravity feed into this tank. When the tank reaches a certain level the pressure head from the sensing tube will cause the valve activator to send a signal to our vacuum discharge valve to open. This will allow our vacuum collection system to draw water from the grey water tank. The vacuum discharge valve will close when the pressure head in the sensing tube goes down to a certain level.

A vacuum in the system is provided by a pump recirculating the liquid in the BW Tank through an educator.

The Problem / Proposed Cause

The proposed cause of air being drawn into the Vacuum Collection System was due to an exhaust fan in the space being set to high while the intake fan remained at low. This caused a vacuum in the machinery space which apparently caused premature pressurisation of the sensing tube tube to act as if the pressure head was great enough to cause the Valve Activator to open the Vacuum Discharge Valve eventually allowing in air.

What I cannot wrap my head around.

I can't seem to understand how a vacuum in the space would cause over pressurization of the sensing tube? I would think a positive pressure in the machinery space would cause that.

Is there some sort of law in physics that can explain this for me? Or does the proposed explanation have flaws?

As you have stated, a partial vacuum in the grey water space could be causing the water level in the pressure sensing tube to rise. It’s drawing water up the tube. The actuation level is probably set for atmospheric pressure in the grey chamber.

Level Probe from Wikipedia

If your sensing tube has barometric compensation, the air pressure would have no effect. If not, then a drop in air pressure would be interpreted as a drop in liquid level. It's just working from an assumed air pressure. So it kind of makes perfect sense what you are saying.

Can you estimate the air pressure change? If so, compare it to the change in head pressure needed to trigger the vaccuum discharge.

When I look at your scheme, there should be no influence between the two systems. (no connection)

You state that there is an influence. So there must be a connection. If the air pressure in the machine space room falls, a deformation off the tank may occur. This could possibly be the cause.

Sensing absolute pressure alone, accurately, is a pretty tricky endeavor that is quite hard to perform. What is almost universally done, is sensing relative pressure; pressure differential - you have a membrane between two chambers, and it deflects (balloons) towards one chamber or the other; measure the deflection and you have the pressure difference between the two chambers. In case of barometers, one of the chambers will be a sealed can containing gas at "reference" pressure, say, 1 atmosphere sharp, and the other is just the open world around - and so the barometer measures how much higher or lower is the atmospheric pressure around you, than the reference "1 atmosphere".

In sensors with barometric compensation, one side will be a sealed can like above, the other will be a sensing tube, where rising liquid level will increase the pressure and deflect the membrane, providing pressure -> level measurement.

In sensors without barometric compensation, one side is the sensing tube in the tank. The other side is open to the room around, assuming some "common" pressure; additionally, if the pressure in the room rises, the same pressure that is pushing the membrane against the rise of water level, will typically push against the reservoir water surface, equalizing everything neatly so only the water level difference between the reservoir and the inside of the sensing tube creates a difference in the pressure.

But in your case, you have a mostly-sealed engine room, and a separately sealed greywater tank. So you're comparing the pressure caused by water level, offset by atmospheric pressure as equalized with vents, siphons, toilets, the rest of the plumbing, vs pressure within the engine room, which might be dropped due to the fans operation - and can't influence the pressure inside the tank, unless there's some "open" connection between the engine room and the plumbing (which I doubt there will be as it would absolutely stink up the engine room.)