The Assassin's Teapot: How Does This Thing Work?

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I'm struggling to figure out the physics here.

This novel teapot of Chinese orgin has two chambers. You can see that when you look down the spout:

So put regular tea in one chamber and poisoned tea in the other. Pour as needed. 

Each chamber has a small hole hidden on the other side. Covering one hole prevents liquid from leaving its chamber. But how? Redditor AjBlue7 explains:

Yes the reason why water flows through a spout is because there is a second hole in the back where air can come in and push the water out of the container. If there are no external forces but gravity working on a liquid there is a high chance that the molecular bonds will be able to resist the gravity trying to pull it out of a spout. Also it is important that air can't get past the liquid through the main spout. So this teapots spout has the equivalent of 2 straws branching out from the main hole, and the spouts much maintain a thin strawlike tunnel all the way down to the base of each reservoir. The connection of the straw and reservoir happens at the bottom of each to decrease the possibility of air being able to get past the water in the straws. Air is lighter than liquid so any air trapped in the back of the reservoir before putting your finger over the hole will always stay separated and not force the water out of the container.

This is one of the main principles at work in diving bells, where they trapped air underwater in a big metal bell. To fill the bells with more water they had heavy barrels with a hole on the bottom to let water in, as the barrel sank water would trap the air in the barrel compressing it naturally as it sank. On the top of the barrel there was a hose that hung on the outside, as long as the end of the hose was lower than the barrels hole that let water in, the air would remain trapped. Then they would raise the hose up and into the diving bell allowing for the barrels compressed air to transfer into the diving bell. Oh and they also had a valve on the top of the diving bell to release "hot" air, aka the CO2 byproduct from the divers breathing.

I'm struggling to wrap my brain around this explanation. Fortunately, I've spent the past few years building up an immunity to iocane powder.

-via Nag on the Lake