Shouldn't it be "Tomorrow it's February", seeing as tomorrow=/=February only the first day of the month? I'm not a native speaker, though, so I'd love to hear some comments :)
Good question! You are right, "tomorrow it's February" sounds better (and is, incidentally, closer to how it is in Polish, since jutro is an adverb, and luty is technically the subject of the sentence). However, "tomorrow is February" is not wrong either, and you might hear people saying it either way.
In English tomorrow is February and tomorrow it's Febuary are both correct.
It is used when the sentence is like "X is Y" and Y is 'definining' X. "Mój tata jest lekarzem" = the fact that he is a doctor, somehow 'defines' my father. But (someone correct me if I'm oversimplifying here) both X and Y need to be nouns and noun phrases. If we turned Y into an adjective, then we would have "Mój tata jest przystojny" - My father is handsome, no Instrumental.
Maybe "jutro" is a noun as well (it undergoes declension), but think of it here more as of an adverb. Or at least an exception, because no one will neither say "Jutro jest lutym/marcem/lipcem", nor "Jutro jest wtorkiem/piątkiem/sobotą".
Let me just add something that I thought of in another comment:
"Zielony jest moim ulubionym kolorem" (Green is my favourite colour) works as well despite 'zielony' being an adjective, and not a noun phrase. So there may be more exceptions to the noun phrase thing.
EDIT: Although then, maybe you can treat "zielony" as "zielony kolor/kolor zielony" = "the colour green"...
I think that english "The green one" is a noun because of "the" and "one", but that would be translated to "zielony" in polish(wouldn't it be?), so maybe "zielony" is also a noun, not just an adjective.
I don't have any reference for it, it's just my guess.
Tomorrow it's february would be the only acceptable translation of this sentence in english. Tomorrow is February is not correct in english, and, unlike what was said above, "tomorrow is february" is not commonly said by native speakers, and when it is it sounds incorrect.