The latter way would be an excellent way for an exchange to go bankrupt. As slide 17 shows, one of the chains can entirely disappear. That means transactions, such as the one depositing coins to the exchange from the old chain are as if they never happened. So if I have 100 Bitcoins before the soft fork, I can deposit 100 Bitcoins from the old chain to this exchange, sell them for some amount of money (say $10,000), withdraw the money and when the chain disappears, the exchange is out $10,000.
There are two ways for an exchange to announce support of trading in a split chain. One way is being done already with Bitcoin Unlimited at Bitfinex and that’s using a futures market. The other way would be to actually trade the coins on both forks.