Tidak is a very definite word in indonesian and almost has the connotation of "not ever." For something that will obviously happen in the future, "not finished" should translate to "belum selesai" instead.
You are right, but don't you agree that "I am not finished" should be translated "saya belum selesai" and not "saya tidak selesai"? In the context of, "This project was not finished" tidak could very well be used, "proyek ini tidak (ter)selesai." Maybe the sentence itself should be changed to avoid this ambiguity?
I'm just talking about this specific phrase "Tidak selesai" and if you translate this with ""belum selesai", it will be accepted as well, but it's simply not the most accurate translation of the negation word 'tidak'.
tidak = not.
belum = not yet.
Regarding your other examples, it depends on context what the most accurate negation word is when translated into Indonesian.
"I am not finished"==> it seems that you're implying that it's not yet finished, but it will be finished (in the future), and yes ...in such a situation 'belum' is more accurate.
The way I see it is that English sentence omits the word 'yet' , 'yet' seems to be implied.
Saya belum selesai ==> I am not yet finished.
That would be my translation from ID to EN.
I would not omit 'yet' in my EN translation.
My EN sentence would be ambigous without the word 'yet'.
Compare the following sentences:
1) "Tugasnya tidak selesai" = "The task is not finished/completed."
2) "Tugasnya belum selesai" = "The task is not yet finished/completed."
In sentence 1) the task is not finished (and will never be finished, for whatever reason.)
In sentence 2) the task is not finished at this moment, but it might be finished/completed in the future.
I think the most accurate negation word depends on context.
In a (minimalistic) phrase like the one from the lesson, there is no context.
More info here about negation words here :
Negation: Tidak, bukan, jangan, belum, Tips & Notes, Addendum.