I think it's an odd style decision. Typographically, a double hyphen is equivalent to an em dash, which means that the punctuation in your first example is equivalent to this:
"But—" Boris tapped his pocket— "your hotel."
Paired em dashes serve to break out a word or clause that can be excised from a sentence without causing the sentence to become syntactically faulty. This, however, is what you get when you drop everything from em dash to em dash, inclusive, in your first example:
"But "your hotel."
which seems to have one quotation mark to many. Another way to break out words or clauses is to use parentheses. But if you substitute parentheses for em dashes in the example, you get this:
"But(" Boris tapped his pocket) "your hotel."
and I doubt that anyone, including Donna Tart, would think that punctuating a sentence in that way would be a good idea.
The most unobtrusive way to punctuate the example would be to use commas. The normal U.S. style would put the first comma inside the first close-quotation mark:
"But," Boris tapped his pocket, "your hotel."
The normal UK style, I believe, would put the comma outside that close-quotation mark. If I wanted to use em dashes instead of commas, I would do it this way:
"But"—Boris tapped his pocket—"your hotel."
and if I wanted to use double hyphens instead of em dashes, I would put them in the same places as the em dashes above.
Having said all that, I acknowledge that punctuation is not a matter of grammatical right or wrong. It is extremely flexible and its applications are highly variable. The two most important things to bear in mind when choosing punctuation, I think, are (1) to use it in ways that make your (or the author's) meaning more intelligible, rather than less; and (2) to enforce your punctuation choices consistently enough that readers don't repeatedly find themselves in the position of puzzling over unexplained internal variations.
For example, in two of the three examples you provide, the second double hyphen in the pair is followed by a letter space (pocket-- "your and eyes-- "I) but in the other one there is no letter space (nose--"global). Although most readers won't notice or care about tiny discrepancies like that one, I think that an author who effectively calls attention to his or her punctuation by making unorthodox choices needs to be especially vigilant against erratic enforcement of those choices. Otherwise, the result is distracting—like watching a film in which an actor fades in and out of an adopted accent.
Readers are extraordinarily adaptable, so an author can make extremely odd decisions about punctuation, as Céline did with his endless ellipsis points, and still be thoroughly intelligible. In my opinion, authors who want their ideas, and not their punctuation, to be the focus of their readers' attention would do well to punctuate unobtrusively. But they should strive for consistency in their approach to punctuation, regardless of how flashy or unusual it is.