No magic and the same photons, but you can have the hardware sensor read them out differently. Specifically using varying amounts of analog gain / amplification before doing analog-to-digital conversion, minimizing noise. This varies based on camera design.
The article mentions the Sony A7S as an example, with the sensor showing marked improvements in SNR when reaching ISO 100, 200, 1600 and 3200, while behaving ISO-invariant wrt. noise in between those values.
Many cameras let you set the ISO in 1/3 stop increments, but if I recall correctly, many camera manufacturers just keep the sensitivity at the base stops and adjust the brightness via software.
So shooting at ISO 250 really means ISO 200 (underexposing what you requested) but then adding a third stop equivalent of brightening to the digital file. Conversely, using ISO 160 actually means the camera is using ISO 200 (overexposing) and lowering the brightness in software.
What this means, at least 10 years ago when I was more in tune with the photography world, is that people would prefer to shoot at the [base ISO stop - 1/3] levels to because those were the levels with the least noise near that exposure setting. The cost is you risk saturating more pixels in the highlights.
And for the same reasoning, the ISO setting s 1/3 over the base stops were typically avoided as they were noisier, albeit with slightly more dynamic range.
How does it magically make more photons fit the sensor..?
And why wouldn't you use that same magic at lower iso gain factors?