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It may well be that the student was upset due to frustration with their own performance and had nothing to do with you or with being cut off. Their actions may not reflect unprofessional behavior as much as just immaturity. Frustration often boils over into anger and the anger is often misplaced. You may have experienced this yourself, actually.

I don't think you need to be proactive here, though it is fine if you want to be. But your best response is to just listen, even if it is to a rant. If you think that some encouragement is needed you could give that, as well as offering to give suggestions on how to do better in such courses.

But you can leave the next move to them, I think.

It is normal for exams to have time limits.

It is also normal for exams to be stressful for students, and thus I would not worry much about a minor lack of professionalism in this context.

I believe that college should be about more than just grades, and wanted to give the feedback to this student that their behavior was extremely unprofessional.

Beyond the answers you've already received here, it's important to avoid giving feedback when someone is not receptive to hear it.

This student was in the middle of finals week, had a number of exams ahead of them, had just taken a lengthy exam, believed they just performed poorly, and was likely very concerned about their grade in the course and potential outcomes resulting from that grade. They may have had other things going on that you weren't aware of too. They had an emotional reaction to all of that and made their way out of the room. That moment is not a good time for them to be receptive to any instructor policing their tone and professionalism.

If there's a more extreme situation where there's concern for a student's well-being or behavior that's impossible to ignore, that may be a different case where some action is called for, but as for looking upset and stomping, what practically are you going to achieve by giving this feedback? Is the student likely to take away a lesson about professionalism, or will they file it under "I was having an awful day, and then I got yelled at for not smiling about it?"

There may be value in reaching out to the student later to offer encouragement, a listening ear, advice, etc... But trying to provide feedback on precisely how they should behave when they're upset is not going to go well and will not be effective.

Students get upset all the time and the best way is to let it happen. Unless there is something statistically wrong with your exam - i.e. everybody gets a really low mark - there is really nothing to be said or done: there's no reason to believe this is not habitual on the part of the student.

What can be done on your part is keep all records relating to the change in scheduling, if you have such records.

Sometimes people are upset at no on in particular, they just need to work it out on their own. This is one of those things.

You shouldn't reach out to the student unless you really know what you're doing. The student might not be happy about you reaching out and complain to the university. You have no duty to reach out either.

Sometimes instructors offer additional work (such as an extra project or assignment) for credit to let failing students bring up their grade. If you have an actual deal of this sort you can offer, that's a fair reason to reach out. But if the student already got a D, it would be hard for you to move the grade by more than a letter without it being unfair to other students - especially if they didn't know that such an opportunity would be offered! So even if you go above and beyond for this student, their grade would at best be a C, which isn't much better. They're better off just retaking the course. If they retake it with you, it might be a pretty good idea to start a dialog (privately) about what parts they struggle with the most. You can frame it as wanting to improve the course so the student doesn't feel singled out for failing.

Don't worry too much about the time - it is what it is. Some people give extra time at the end of exam - but if you've taken 2 hours to do an exam other people did in 1.5, you've probably had all your best ideas already. Even an additional hour is unlikely to make a difference, unless the exam was specifically designed to gauge speed of work (if it was, you wouldn't have so much variance in how quickly they finish). If the student complains, you can point out that everyone gets the same amount of time, so giving an extra ten minutes is already special treatment for that student at the expense of everyone else who didn't get extra time. You would already take the overall class performance into account when grading, so if everybody had done poorly in that timeframe, presumably the best students could get an A despite not getting every question right.

Also, the final is a bit late for interventions. There's not much graded material left... Unless the student does retake your course, or comes to you for help, there's nothing you can do here - the ship has sailed. For future students, you can play close attention to early midterms and quizzes, and act accordingly during office hours, lectures or when providing study materials. Inevitably, some people in every class will score low. If you really want to prevent this, you can build in "second chance" type rules in your syllabus: For example, option to do a project for extra credit, or dropping the lowest mid-term mark from the average. If you put these in the syllabus and make them clear in the beginning of the course, it's a lot easier to help failing students overcome their low exam score while still being fair.