The simple answer to the (apparent) actual question is
"In “The Martian”, did the <PERSON> leave immediately or wait for awhile?"
Yes, in the movie, they did leave "immediately".
That's the answer.
* the "exact amount of time before they leave" is simply not detailed in the movie. Why would it be? It's a movie, he's utterly dead: so they leave. As an audience we simply interpret it as "He was dead so they left the scene." It's utterly clear that they leave "quickly" (like, "within a few days"). 918
The entire, total, point of the movie and book is that "They think he's dead so they leave."
* Even in the book, there's like one throwaway sentence (in the whole book) dealing with the details of when, exactly, they leave. Note that it would make no difference, at all, if <PERSON> left within a minute, a day, an hour, a week or even a month.
* Note that of course they had utterly no way to get up and down to him. Why stay even if, amazingly, they learned he was alive? Once they pressed the "go" button on the ascender, it was all over for him.
Again, precisely when they leave is not especially discussed in the movie, and I don't see any reason it should be. We "just accept" that (bizarrely) their incredibly advanced comms systems incorrectly thought him dead; we "just accept" that (surprisingly) jpegs can be sent to <PERSON>, we "just accept" that (ridiculously) at the end there was conveniently a hatch to blow on <PERSON>' nose, and so on.
The question here seems to be asking/implying numerous other questions,
* why didn't they spend more time, in orbit, checking if he was dead?
* wouldn't they have (various) technology, from orbit, to be able to check if he was dead?
* what is the detailed nature of Mars orbital spy telescopes?
* ditto for Mars orbital radio, radar etc etc devices?
* assuming it was government policy in such cases to just leave, why would that policy be so?
* with the putative fictional Ion Engines, were they using a <PERSON> transfer?
* if using a <PERSON> transfer from Mars, what window do you have?
* if not using a <PERSON> transfer, what would be their windows of departure?
* why was it limited to a 30 day mission? does that relate to departure windows or was it unrelaed?
* how does the movie plot compare to the book plot?
* in the book specifically, what are the answers to every one of the above questions?
* would <PERSON> be able to stretch food and what is the detail of that?
* numerous questions about <PERSON> return transfer
* etc etc
I'm totally in favour of discussing those issues, but I guess here on SO the SO philosophy is that those should be separate questions. 209