You need a dark sky and a sunlit satellite at the same time, which mostly happens in the hours after sunset and before sunrise.
Two conditions fight each other.
You must be in the dark. In daylight the sky is far too bright to see a small point of reflected light. This site waits until the Sun is at least 6° below your horizon, the end of what the US Naval Observatory defines as civil twilight.
The satellite must be in the light. Satellites shine only by reflected sunlight. Late at night, a low satellite passing over you is inside Earth's shadow and gives off nothing.
Both are true together only for a while after sunset and before sunrise. The Planetary Society's ISS guide says the same: viewing conditions are right only near the edge of Earth's shadow, usually around dawn or dusk.
In November the Sun sinks below Delhi's horizon at roughly 12° to 13° per hour (see the calculation below). Say it sets at 5:30 pm. For about the next half hour the sky is still too bright — civil twilight — so the site lists nothing before about 6 pm.
From then on, a satellite at 420 km height passing overhead is still in sunshine, because from up there the Sun has not set yet. It stays lit until the Sun is about 20° below your horizon — about an hour and a half after sunset, so around 7 pm.
So the best window for low satellites like the ISS is from about half an hour to two hours after sunset, and the same span before sunrise. Around midnight, the ISS can pass right overhead and you will see nothing.
Before searching for passes, the site works out the dark window for your location — the minutes when the Sun is at least 6° down — to the nearest minute. If you open it in the afternoon, it can tell you when it gets dark enough. On the homepage, the Next visible pass panel looks up to 36 hours ahead; if nothing bright enough passes, it says so.
Higher satellites stay lit later into the night, because Earth's shadow is narrower far from the Earth. But most of them are too faint to see — see why you can't see geostationary satellites.
Notice that the pass start times cluster in the early evening and the hours before sunrise, with few or none around midnight. See tonight's passes over Delhi
Sunrise and sunset are defined by the US Naval Observatory as the moment the Sun's centre is 50 arcminutes below the horizontal (a geometric zenith distance of 90.8333°), which allows for refraction and the Sun's radius. Twilight stages are then 6°, 12° and 18° below. The site's sky-state helper uses the same thresholds: above −0.833° is day, down to −6° civil, down to −12° nautical, beyond that night.
How late can a satellite stay lit? Consider a satellite at height h directly above an observer, with the Sun at depression angle D below the horizon. The satellite leaves sunlight when the shadow line — a tangent to the Earth — reaches it. In the simple cylindrical shadow picture, the satellite is lit while cos D > R / (R + h). With R = 6,378 km:
How fast does the Sun sink? Near the horizon its altitude changes at about dh/dt ≈ 15°/h × cos φ × cos δ × sin H, where φ is your latitude, δ the Sun's declination and H its hour angle. For Delhi (φ ≈ 28.6°) in mid-November (δ ≈ −18°), sunset comes at H ≈ 80°, giving 15 × 0.878 × 0.951 × 0.985 ≈ 12.3° per hour. So 6° of depression takes about 30 minutes and 20° about 1.6 hours. At higher latitudes the Sun sets at a shallower angle and these times stretch out; that is why ‘about 1.5 hours after sunset’ is only a rule of thumb.
The dark-window search in the code steps through 24 hours one minute at a time, testing the Sun's elevation with the same Sun formula used for the shadow test, so the ‘dark enough from’ time it shows never contradicts the pass list.
The daytime sky is far too bright for its reflected sunlight to stand out.
At that hour the ISS, being low, is inside Earth's shadow over India, so there is no sunlight for it to reflect.
When the Sun's centre is 6° below the horizon.