The paper is behind a paywall, so I can only infer as to how they measured their level of confidence.

K2-18 is a red dwarf -- the most common type of star in our galaxy. Telescopes like the JWST can read the spectrum of  a star, which is how they can determine the prevalence of different elements in a star. The planet, K2-18b, was discovered through occultation -- blocking some of the star's light as it passed between us and K2-18. The amount of dimming allows astronomers to measure the planet's diameter.

As an added benefit, starlight shining through gases in the planet's atmosphere create absorption lines in the spectrum. If the characteristic lines for DMS or DMDS suddenly appear as the planet transits the star, we know it must be from the planet. You are talking about a planet's atmosphere, 124 light years away -- so, not a lot of photons. Time on the JWST is expensive -- and scarce -- so the signal is very weak. JWST maintains a temperature of <7 K, which is very cold...but there is still heat, and that adds a small amount of noise to the data.

My surmise is that the researchers are sorting through the photons, trying to determine whether they are consistent with the spectral lines of DMS and DMDS (they are similar) or not. In a perfect instrument, this would be straightforward. Add noise and you are looking at overlapping bell curves, trying to assign each photon to one bucket or the other. With enough data, you should have a sample size sufficient to make statistical inferences. With what the have now, they can say that the difference in means is significant to 3 standard deviations. Normally, that would be good news. But 5 standard deviations would be better -- and that means capturing more data.

Anyway, that's my guess on how they do it.