I find it specially difficult to understand how the atoms in the measurement magnetic field colide with the atoms in the vacuum chamber without leaving the magnetic field/device.
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You have a vacuum chamber that has almost no molecules in it. That vacuum chamber has a port on the side of it which opens into the measuring device.
The measuring device introduces a sample of extremely cold atoms (lithium or rubidium are apparently most common) which are caught in a magnetic field and confined to a region inside of the measuring device. But the magnetic field is not much “thicker” then the minimum it needs to be in order to confine the cold atoms. The quantity of these atoms in the measuring device is obtained by observing their fluorescence induced by the trapping mechanism.
The measuring principle is that as the very cold atoms are periodically impacted by the much warmer and much faster moving atoms in the vacuum chamber, they are given enough kinetic energy to escape the trap, and the rate at which they get knocked out of the trap is related to what the pressure is in the vacuum chamber.
Your difficulty might be that you seem to think the atoms in the trap are moving into the vacuum chamber. They are not. The opposite is happening: the atoms that are in the vacuum chamber collide with the atoms which are confined to the trap, which is why you have to connect the measuring device directly to the vacuum chamber. In other words, there is a an opening between the main vacuum chamber and the measuring device, so in some sense, the measuring device is part of the vacuum chamber. Atoms can travel between the measuring device and the main vacuum chamber.
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