Are you sure the Mechanic added real Dex Cool and not stuff that was "Dex Cool compatible"? Dex Cool is red, regular stuff is green, then you have the orange that Bill references that is compatible with both. Most garages use the Orange so they don't have to stock multiple fluids or worry about what they are putting into what.
If he added the orange fitz-all you will be fine, no worries. might be worth a phone call to double check on what he added before you go to the trouble of re-doing the flush.