Not sure about Delta's written policy, but Continental states in their 'extra seat' terms that it's the customer's responsibility to ensure their extra seat is not taken by another passenger - that means informing the GA and FA that you have an extra seat purchased for yourself (so they don't accidentally put a standby there), and preventing a passenger from plunking themselves down in one of your seats.

On aircraft where the exit row has movable armrests, should you take two seats, make sure you don't select an aisle and leave it vacant as your 'spare' seat. Take the window and middle or aisle and middle (and sit in the aisle).