Learn English – “he leaves for New York tomorrow”. vs. “he will leave for New York tomorrow”

Both are grammatically correct.

Yes, you can use such words as tomorrow, this evening, later today, next month, five years from now in sentences that refer to future time.

But there is no "future form" in English. The simple present tense form of to leave is leave/leaves (he leaves); the simple past tense form is left (he left); the simple future tense form is ??????. English does not have one.

If there were a future tense form of leave we could just write it, something like leavek (he leavek).

To say will leave is the future (tense) form is to arbitrarily choose one of over a dozen ways to refer to future time as "the future form".

Actually, the modal will expresses current resolve:

I will leave for New York tomorrow

expresses the current resolve of the speaker to leave for New York tomorrow. As such, it is a promise. Even such statements as The sun will rise tomorrow and That kind of thing will never happen here are promises.

Thus

I don't know when he'll (he will) leave tomorrow

expresses the speaker's ignorance of the exact time tomorrow that the person he will fulfill his resolve to leave. He has made his resolve known, but perhaps he has not stated at what time tomorrow he will carry it out.

We use the simple present to talk about future time with the strongest certainty. Things we are absolutely convinced to happen:

The sun rises tomorrow at 0626.
The train arrives tomorrow.

He leaves for New York tomorrow is the way to say with the strongest certainty that in the future time designated 'tomorrow', the person he => /leave/ for New York.

Thus

I don't know when he leaves tomorrow

expresses your ignorance of the exact time that his leaving happens. You know he's leaving tomorrow, just like you know the sun's rising tomorrow, but you don't know when tomorrow or at what time tomorrow.

How else can we refer to future time? Here are some ways:

He's leaving for New York tomorrow.
He's going to leave for New York tomorrow.
He's going to be leaving for New York tomorrow.
He'll be leaving for New York tomorrow.
He is to leave for New York tomorrow.

There are others.