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As the article states a "void" is a region where there is less mass or energy than its surroundings. The void is manifested as a cold spot on the cosmic radiation background.
The cold spot mechanism has a somewhat subtle connection to the slowing down of clocks in gravitational wells as exemplified by the GPS time corrections of satellite clocks to keep them synchronized with Earth clocks.
A clock located on the Earth's surface runs slower than a clock on an orbiting satellite. This is a result of gravitational time dilation as the Earth's clock sits deeper in the gravitational well than the satellite's clock.
Similarly a photon located deep in a well is gravitationally blue shifted when compared to a photon higher up the well It has more energy the deeper it is in the well. A photon moving up the well gains gravitational potential energy and loses kinetic energy, the situation is reversed moving down the well.
If the void is at non cosmological scales, the CMB photons would behave as if they were in the Earth's gravitational well.
A photon entering the void will gain gravitational potential energy but lose kinetic energy, on exiting the void kinetic energy is gained but gravitational potential energy lost. Since this is symmetrical there is net loss or gain in energy and there is no change to the CMB relative to the observer.
If the void is as cosmological scales (very very big) the void will stretch out as space expands. It means the energy density decreases as space expands and well as the energy difference between the void and the surrounding region. Since photons occupy the void at time scales long enough for the void to expand, photons entering the void lose more kinetic energy then gaining the energy when exiting it.
As a result CMB photons are more red shifted which appears as a cold spot on the CMB relative to the observer.
Steven
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