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.
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"...