Educational question: How do international-focused funds determine their value after 4pm US market close?

Vanguard tells me that if I place an order for let's say VTIAX before 4pm eastern time, I'll get the price determined at the 4pm closing. But international stock exchanges will be largely closed by that time, and the price of stocks will change upon reopening. How can a mutual fund company promise a certain price, when they aren't able to buy the securities yet for this purchase, and risk having to buy at a higher price the next day?