Is night consider sunset even tho the sun ain't down?

The night rally started when the star appear, so it would take around 10 to 15 minutes after the sunset time.

WHEN  you see sunset  it is actually  BELOW  the  horizon and the light is bending in the atmosphere

so yes even though you see light  the  sun is actually below the horizon

Precise definition depend on why you are using a word.

In nautical astronomy, "sunset" happens when the centre of the Sun's apparent disk is exactly 90 degrees from the zenith. That distance (90 degrees from the zenith) is how you define the theoretical horizon.

Back when this was developed, ships were relatively low. The sea horizon, as seen from the deck of such a ship, was quite close to the theoretical horizon. Also, calculations - in spherical trigonometry - involving angles of 90 degrees were A LOT easier than the general formulas.

Therefore, it was accepted by all (navigators and astronomers) that sunset happens at that moment. There are (at least) three things that kill the magic of that moment:

1) the eye of the navigator is never exactly at sea level. There is a tiny difference called "the dip of the sea horizon" - usually a fraction of a degree, that gives the appearance of raising the position of the Sun's centre, relative to the horizon.

2) The image of the Sun is refracted by the layers of the atmosphere, causing it to appear higher than it really is. Depending on the conditions (air pressure and air temperature) this difference could be as much as a full degree.

3) When the centre of the Sun is on the horizon, we are still getting sunlight directly (from the top half). For normal people, it is definitely not night!

Therefore, navigators made their "sunset" observations when the Sun appeared to be 1.5 times its diameter ABOVE the sea horizon (definitely not sunset for normal people).

In the distinction between "night and day", night begins when the top of the apparent Sun finally dips below the horizon. Night is separated into different parts, depending on how much light we still get (indirectly).

Civil Twilight: from sunset to when the Sun is 6 degrees below the horizon. Sunlight still reaches the bottom layer of the atmosphere (up to the tropopause) which gives enough light to continue our activities "as if" it was still daylight (this is the source of the "30 minute" grace period given in different regulations).

Nautical Twilight: from the end of Civil, to when the Sun is 12 degrees below. The Sun is still shining on the stratosphere. It is now dark enough to see the brighter stars, and yet still bright enough to see the horizon (at sea). That is the interval during which navigators use the sextant to measure the altitude of navigation stars to calculate the position of the ship.

Astronomical Twilight: end of Nautical to 18 degrees below. We humans find it dark but the sun is still shining on the exosphere, just enough to be detectable in long-exposure astronomical photographs.

And the same thing happens (in reverse) just before sunrise.

In nautical astronomy, "night" includes all three Twilights at both ends. In the application of most civilian laws, "night" begins at the end of Civil Twilight in the evening (dusk) and ends at the start of Civil Twilight in the morning (dawn).

And there are other usages of the word "night"

Night is after sunset. The Talmud defines it as when three second magnitude stars are visible in the sky, so there would be some variation, but that makes sense to me.

'Evening' covers the time between 

when the sun is approaching the 

horizon, and the time that it sets. 

'Twilight' comes after sunset 

(when the Sun is below the horizon) 

and 'Nighttime' comes after twilight. 

Night time begins when the Stars come out

If you are talking non astronomically, then night comes after "evening". "This evening" means after the sun had gone below the horizon and an hour into the darkness (depending on whether it's Winter or Summer) as in "Shall we go to the movies this evening or watch TV?". "Night" is used mostly in the terminology "tonight" as in "What are you doing tonight?". This gives you an idea from two hours after sunset (already dark) until bedtime.

Smart people have actually already nailed these things down. Like, hundreds of years ago.

ICAO and FAA regulations consider 30 minutes after sunset and 30 minutes before sunrise to be the triggers between day and night. That thirty minutes in both directions, going into and coming out of night time, to still have some light due to the twilight effects you're talking about.

So by aviation standards (ICAO and FAA) its daylight thirty minutes before sunrise and thirty minutes after sunset.

here's a page that defines what 'night' is...  Before Sunrise, and after Sunset, there's a period of 'twilight'... when the sun is far enough below the horizon, that's when "night" is...

https://www.weather.gov/fsd/twilight