Hmm. I'm not so sure about that. There have been occasions in the past where I've been lambasted pretty harshly because I wrote about someone or their work and didn't notify them or send them a copy. So notifying or not notifying seems like a no-win situation. If you let them know you didn't like their book, it's rude. If you don't let them know you didn't like their book, it's rude.
Personally, I'd want to be notified, even about a negative review. Discovering such things by Googling my own name -- yes, I Google myself once or twice a year, and, admit it now, you Google yourself too -- feels a little over-egotistic.
I suppose it depends on the tone and content of the negative review. When I don't like a book, I try to be valid, specific and constructive about the problems I had with the book. I also try to be phrase my words politely and as painlessly as I can. (Sometimes this is difficult. Some of the books I've reviewed on this blog have been *ahem* very poorly written.) If someone discusses my own writing with a similar approach, I'm (probably) not going to be annoyed.
There's a reviewer on Goodreads who writes about quite a few YA titles, and whenever I see her name heading a review, I can be pretty certain she'll be going at that book (and its author) with all guns blazing and foul language rampant. She goes at books and their authors with ax and chainsaw, gasoline and matches, and then finishes by pissing on the smoking ashes. As performance art, it's kind of impressive in a stunned, jaw-dropping way. As book reviews, any valid criticisms she makes (she does make some) tend to be vastly overshadowed by the ugly invective and inappropriate rage she brings to her reviews. That may be the kind of "negative review" Ann Leckie's tweet is referencing.
(Ann Leckie's kind of a special case. ANCILLARY JUSTICE, and its sequel ANCILLARY SWORD, have been some of the most widely discussed and reviewed books that have come out in the past several years. If she read all the reviews and opinions people have written about her work, it'd probably be at least a part-time job on top of her normal life.) (Not a problem in my own case, certainly, with my most-recent published story way back in 2006. Self-Googling generally catches only one or two fresh comments a year about my old stories, usually "Death and the Ugly Woman" from 1986. Another reason, I suppose, to hope some of the new fiction I've been writing sells and gets out there to be read.)
So... if I write a review of your book, even a critical or negative review, I'll probably let you know about it. (That actually depends on how organized or time-pressed I am on any particular day; that varies, well, a lot, and usually not on the side of efficiency.) [I suppose if I'm going to write about people's Twitter posts, I should actually sign up for Twitter, to be able to respond directly to their tweets. I think I went a little over 140 characters with this post, though.]