What you have to remember about the witches is that they are "juggling fiends", that "palter with us in a double sense" - that is, that what they say is elliptical and difficult to decipher. So that what it seems like they mean is not always what they mean. (Shakespeare's language in "Macbeth" often also fits this description.)
Macbeth's death does, of course, follow the witches predictions. He is killed by Macduff, as per prediction 1: "Beware Macduff; Beware the Thane of Fife".
Macduff also reveals shortly before killing Macbeth that he was born by Caesarean section, "ripp'd" from his mother's womb rather than being "born", bringing true the witches' second prediction: "for none of woman born
Shall harm Macbeth".
And lastly, Malcolm's troops tear down branches to screen them as they approach his castle, which certainly gives the impression of prophecy number 3 coming true.
Macbeth shall never vanquish'd be until
Great Birnam Wood to high Dunsinane Hill
Shall come against him.
Their original prediction - that Banquo's sons would become kings - is actually something of a meta-theatrical one. James I, on the throne when "Macbeth" was written, was thought to be a descendant of Banquo's. So the play doesn't explain how - but if you were in the original audience, you'd know that that prediction was also an accurate one.