He is working on Tuesday, but I don't know when he finishes/ will finish. Both are OK, but native speakers usually use present for future in such dependent clauses. Notice that you used a present verb form for future in your first clause also.
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Mister Micawber He is working on Tuesday, but I don't know when he finishes/will finish.I'm curious to understand why you have used continious(... is working ...)
I suppose that as th
He works/will work on Tuesday, but I don't know when he finishes/will finish
The Present Continious is used to express
He arrives London on Monday
We return home tomorrow
They will buy a new car soon - correct
They are buying a new car soon - sounds good
They buy a new car soon - seems to be mistaken
The steamer sails tomorrow - should be correct