It is referring to a time in the future when what he does will be in the past.
You don't know if he has already done it now, and you are just waiting for a time in the future to see what it is, OR
If he is currently working on it, and in the future, you'll see it completed, OR
If he hasn't started yet, and in the future you'll see it completed, OR
Any of these things and it will still be a work in progress then.
Since it says "near future" I would guess that whatever it is, it's already done, and very soon you'll see what.
At that time, we'll see what he has done. It's simply not know what has been done NOW.
Do you mean that "has done" is referring to the future just as how present tense is used for the future in "we'll see how it goes"?
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