I'd guess they have a pool of dollars at hand, in the form of a liquidity pool, to accommodate anyone who takes out a loan in dollars. Of course, they can only predict demand on the platform so well. If this is the case, and they need more dollars than are available in their liquidity pool, they would likely need to turn to a larger market maker, and sell a surplus of some other asset that isn't expected to experience such immediate demand.
Then once the immediate dollar demand is accounted for, and they get the impression that dollar demand has leveled off in the short term, they may choose to rebalance their liquidity pools based on precedented demand.
Just speculation though. Really I'd like to better understand how major exchanges deal with stuff like this.