Both смотрел and посмотрел are OK in this sentence.
Not sure if it is "experiential perfect" or something else... Maybe in my previous message, I confused myself a bit.
So... We talk about some state that established in the past and continues to be actual up to the present (and possibly will be actual forever).
A state can be:
1. A result of a logically completed action, i.e. result of a perfective verb.
As in our example: the man "посмотрел" the movie, so the state "the movie is watched" is actual for him now and forever.
2. Just a fact that some process took place in the past.
"Я был в Америке." - the process "был в Америке" was in the past, but this sentence itself means not only "process was in the past", but also the fact that the state "был в Америке" is actual for "я".
That is a usual way of talking about "a thing that is going at some time or after another thing". Compare:
Что ты будешь делать сегодня вечером? -> Сегодня вечером я буду писать письмо.
Что ты будешь делать после ужина? -> После ужина я буду писать письмо.
Что ты будешь делать, когда прочитаешь эту статью? -> Когда я прочитаю статью, я буду писать письмо.
"Сегодня вечером", "после ужина" and "когда я прочитаю статью" all are adverbial phrases denoting when the process is going.
The speaker just says what will be happening at the specified time, but she does not mean that the process will be leaved incompleted.
Perhaps it will become clearer if we reword that dialog in pseudo-English:
- What will you be doing (process) when you will finish reading (instant action) the article?
- When I will finish reading (instant action) it, I will be writing (process) a letter.
- What will you be doing (process) when you will finish writing (instant action) the letter?
- When I will finish writing (instant action) it, I will be watching (process) TV.
(A side note: in fact, когда means "after" when used with a perfective clause.)