You must have visited him last week, didn't you?
You must have visited him last week. Did you? This is still strange. If you know that he must have visited him last week, why ask whether he did. Simply ask "Did you visit him last week"
You must finish it today, mustn't you? (obligation)
You must finish it today, needn't you? (necessity)
"Do you need to finish it today?"
The boys mustn't play with fire, may they? (prohibit) Is this from your text book?
"The boys musn't play with fire". or "May the boys play with fire?" but not both.
You must come tomorrow, will you? (invitation)
"Will you come tomorrow?"
"You will come tomorrow, won't you?"
You must be kidding, aren't you? (confirm)
"You must be kidding" OR "You're kidding, aren't you?"
He must have waited for long, hasn't he? (guess what happened in the past).
"Did he wait for a long time?"
Or let your statement remain with "He must have waited a long time".
There's no need to postulate any "musts" at all with these questions
What does your grammar book actually say that is confusing you?
Student or Learner