At this point it is likely that your new fish has shared anything he has with your tank. White dots can be caused by many things, (ich, lymphocystis, amyloodinium, brooklynella, sand, and even just air bubbles), so making the assumption it is ich is not usually a good idea. Its important to observe the fish closely and take note of all symptoms, particularly since not all of the conditions that can cause white dots require the same treatment or quickness of action.
It could be lymphocystis, in which case good food and clean water and it will go away on its own. If it is ich you need to remove ALL of your fish to a hospital tank and treat with copper, hypo, or tank transfer method, meanwhile leaving your DT fallow for eight weeks. Ich will NOT go away on its own, it will continue to live in your system infecting your fish. There are no effective treatments that are safe for invertebrates.
Quarantine of new additions prior to introduction to the DT would allow you to avoid situations like this in the future.
