No, I don’t think your understanding is correct. The present perfect infinitive “to have done” expresses an accomplished action. An obligation to accomplish something that has already been accomplished is not grammatically logical in English. “Must” is what is called an imperfect verb because it cannot be used in all the tenses. “Have to” is used in the tenses where “must” is not used. Sometimes they are both used in the same tense with approximately the same meaning. I have to do it. I must do it. He must have done it…..formal He has to have done it…. colloquial The above pair both have the same meaning “he most probably has done it.” To express a past obligation "had to" is used not "must" (except in reported statements). He had to do it….It was his obligation. He had to do this job by yesterday. Other ways to express a past obligation for a theoretically accomplished action: (There are probably a few more.) He needed to have done it. He was supposed to have done it. He should have done it. He was obliged to have done it. Don’t confuse the above with the causative use of have. He had to have it done.

"had to have done" is not used. Try: He was supposed to have finished it by yesterday. "must have" refers to likelihood, usually high probability.

*responsible; *meets deadline