The door and the wind are southern because of the tilt of the earth's axis. No, really.
Bengal is a bit north of the Tropic of Cancer. So the sun is always in the south and never directly overhead. Houses there naturally have their greatest sunlight exposure in the south. To maintain heat and light as efficiently as possible during the winter, the main door would be south-facing.
The poem's setting is early spring. Tagore speaks of নববসন্তের প্রভাতের আনন্দ / navabasanter prabhaater aananda, the joy of daybreak in early spring:
How can I transmit to you who are so far away
A bit of the joy I feel this day,
At this new spring dawn
(Fakrul Alam's translation at Sunrise Ranch)
Since a garden north of the house would be in shadow all year round, gardens would be south of the house. Early spring is when flowers just begin to bloom again. So a breeze from the south is what would carry the fragrance of flowers.
১৪০০ সাল / The Year 1400 was published in Tagore's 1896 collection চিত্রা / chitraa, a star in the constellation Virgo. The date of composition printed after the poem says ২ ফাল্গুন, ১৩০২ / 2 Phalgun, 1302. That corresponds to Valentine's Day 1896 in the Gregorian calendar. Tagore is wondering about the reception of this poem roughly a hundred years later, in the Bengali year 1400 / Gregorian year 1994.
In 1913, Tagore published 85 poems in his own translations from the Bengali in The Gardener. His very abridged recasting of ১৪০০ সাল / The Year 1400 was included as the last poem in this collection. This is the version at the Poetry Foundation site.
Kumud Biswas's translation of the entire poem is at AllPoetry, and Fakrul Alam's at Sunrise Ranch.
The translations by both Biswas and Alam are competent enough. It's hard to capture Tagore's effects in translation, though; even he pretty much sucked at it. Take for instance the lines you cite about the southern breeze:
উড়ায়ে চঞ্চল পাখা পুষ্পরেণুগন্ধমাখা
সহসা আসিয়া ত্বরা রাঙায়ে দিয়েছে ধরা
u.Daaye chañchal paakha puShpareNugandhamaakhaa
sahasaa aasiyaa tvara raaÑgaaye diyechhe dharaa
Spreading its restless wings
The southern breeze blew
Carrying the scent of flowers’ pollen
All on a sudden soon
They coloured the world with a youthful glow
Alam translates, taking rather reckless liberties with the order of the lines (and therefore the semantics) of Tagore's original:
There could blow with the southern breeze,
Impatient and eager to please,
Flying on restless wings,
Full of pollen and the scent of flowers,
And of what youth desires,
An impulse ...
Impatient and eager to please are from an earlier line, as is an impulse. There could blow is definitely not what Tagore wrote; Biswas has it right with blew. But this is not to fault Alam's translation qua translation; those choices are his to make.
The point is merely that neither translation quite gets it right in the way that Tagore does. Here's a literal translation:
The south wind, flying on excited/fleet/mischievous wings anointed with the fragrance of pollen, has suddenly, swiftly painted the earth in the colors/melodies/desires of youth.
Two words that defy simple translation are চঞ্চল / chañchal and রাগ / raag. The former means something that's light-hearted, high-spirited, fickle, swift, mischievous, excited, and sharp. Think of a shying young deer with a playful sense of humor, and you get something of the sense of the word.
The line যৌবনের রাগে / yauvanera raage means in the raaga of youth. That word raaga can mean three things. First, it can mean color, and that's the most fundamental meaning here. Biswas translates it as "youthful glow", which is close enough.
Second, it can mean a melodic mode. Indian classical music is based on the concept of raga. Wikipedia says:
A raga or raag (IAST: rāga; also raaga or ragam; literally "coloring, tingeing, dyeing") is a melodic framework for improvisation akin to a melodic mode in Indian classical music.
Third, it can mean an overmastering impulse, something that takes over one's mind. Alam gets it right when he speaks of "what youth desires", because young sexual desire bubbling over as springtime sets in is in fact the overwhelming force here.
Translations can't capture that sort of polysemy, but a Bengali reader would immediately be affected by all three meanings, as they all apply here. Translation also misses out on the synesthesia. The breeze is anointed (মাখা / maakhaa) with fragrance; scent and touch both operate here. As for রাগে / raage, that gets sight (color), hearing (music), and the psychophysical state of sexual desire.
Essentially, through such paronomasia and synesthesia, Tagore gathers up the entire sensory and affective experience of the early spring dawn in a couple of well-chosen phrases, and wonders how his poem can communicate that experience to some reader a hundred years hence. His original Bengali succeeds pretty admirably. The translations, nice try, but not so much.
Two Chitras, two Chitrangadas
The 1896 Bengali collection Chitra in which this poem first appeared has nothing to do with Tagore's 1913 play Chitra. The latter is his translation of the 1892 Bengali play চিত্রাঙ্গদা / chitraaÑgadaa, based on an episode in the Mahabharata.
To complicate matters further, late in his life Tagore wrote a dance drama depicting the same Mahabharata episode, and called this play chitraaÑgadaa as well. The Bengali-language Wikipedia says:
নৃত্যনাট্য চিত্রাঙ্গদা হল রবীন্দ্রনাথ ঠাকুরের লেখা প্রথম পূর্ণাঙ্গ নৃত্যনাট্য। ১৯৩৬ সালে কলকাতায় অভিনয়ের উদ্দেশ্যে প্রকাশিত এই নৃত্যনাট্যটির সঙ্গে ১৮৯২ সালে রচিত চিত্রাঙ্গদা কাব্যনাট্যের বিষয়বস্তু ও তত্ত্ব এক ও অভিন্ন।
Dance Drama Chitrangada is Rabindranath Tagore's first through-composed dance drama. Published in 1938 with an eye to a Calcutta performance, this dance drama entirely shares its subject and theme with the verse play Chitrangada that had been published in 1892.
Lopamudra Banerjee has translated the script of the dance drama. A performance is available on YouTube.
Of course none of this has anything to do with the poem, but it's useful data to bear in mind. Tagore really needed to be more creative with his titles.
Transliteration of Bengali above follows iTrans.