My DH and I share an account on Kindle. We've never yet read the same book at the same time. I have so many books on the account, I can't see it would ever crop up, to be honest. Usually DH will read a book after I've read it. Because I like to be able to access my current book on my iPhone (in case I'm out and have forgotten my Kindle), I do like the sync to furthest page read feature activated.
When I've finished the book, I log into my Amazon account on my laptop, go to 'manage my content' or whatever it's called, and then reset the furthest page read for that book. I then open the book on my Kindle, go to the first page, and close the book. It will now sync to that page, all ready for my DH to read.