Must refers to a necessity.
In the present or future tense, it can sometimes indicate a matter of fact ("what goes up, must come down") and sometimes of obligation ("you must pay your taxes"), or merely exaggerating what is not a necessity by describing it as such ("you simply must see the production of Coriolanus at the Donmar Warehouse if you're in London, it's superb")*.
With the perfect tenses, must indicates a matter of fact, that has been deduced.
He must have been here recently, the kettle's still warm.
Now, "matter of fact" does not necessarily mean it's true; but if it isn't true, it's because the deduction is incorrect: We're confident of our deduction.
It can also be used to state a deduction of what must follow in a particular case:
If he had been to the club, then he must have seen her.
This puts forward that in a certain case ("he had been to the club"), then a certain fact would follow ("he saw her"), though in itself it doesn't state that he had been to the club, so it allow for both parts to be false; again what is expressed is a deduction about how one thing would follow from another.
*And it was, but it ended last Saturday.