Think of it this way:
He left for Mumbai on Sunday (expecting) to arrive there on Monday.
This would be said before the speaker learns that he arrived, so his arrival is an expectation not a fact. At the point of the statement, the speaker knew he left, so there is no reason not to use simple past. The tense of left doesn't change.
Where perfect tense could be used, because there is a later concrete action:
He had left for Mumbai on Sunday, but because of a sudden emergency at work he needed to return Sunday evening.
If the statement was made after the speaker learned of his arrival, then:.
He leftleft for Mumbai on Sunday and arrived there on Monday.
As uncertain/predicted activity in the future (let's say he is telling his boss about a co-worker's travel plans), you could use:
He is leaving for Mumbai on Sunday, arriving there on Monday.