Becasue it is the Dragonhawks trigger that exiles the cards that also sets up a delayed trigger for the damage at end of turn. Dragonhawk could leave the field before the cards are even exiled, and it would not matter. The ETB trigger and the delayed trigger are both independent of it.

and for how Dragonhawk can deal the damage when it is gone? Becasue the rules say that it can:

113.7a Once activated or triggered, an ability exists on the stack independently of its source.
Destruction or removal of the source after that time won’t affect the ability. Note that some
abilities cause a source to do something (for example, “This creature deals 1 damage to any
target”) rather than the ability doing anything directly. In these cases, any activated or triggered
ability that references information about the source for use while announcing an activated
ability or putting a triggered ability on the stack checks that information when the ability is put
onto the stack. Otherwise, it will check that information when it resolves. In both instances, if
the source is no longer in the zone it’s expected to be in at that time, its last known information
is used. The source can still perform the action even though it no longer exists.