I have no experiences of adding a new mandarin to a tank there is already an established individual of the same species. I have a general experiences of adding new fish into my 8 years old aquarium. I always start that process with having the newcomer either in my refugium, sump or in an adaption box (a freshwater guppy breeder floating box) for 5 - 10 days. This will normally make the introduction into the DT without any aggression at all. Because this works both when my old fishes can see the new and when they can´t, I believe that it is the smell that matter.
However - a month ago I a friend of mine shout down his aquarium and he had - among other things I wanted - a percula clown of the same size as I already had in my DT. He ask me to even take this clown but I hesitated because I saw it as an impossible task. At last - I decided to try this "mission impossible". In this case - I believed that not only the smell was important - they have too see each other. My guppy breeder box was placed in the DT with help of 2 magnets. The clown and another newcomer was placed there. It took 5 sec - and the old clown was aware of a competitor. It start to attack the new one from the outside - and the new one attack from the inside - but there was a wall between them - they was not damaged. They fight each other for nearly every minute the light was on for 5 days - from each side of the box. The fight seemed to have different stages and on the fifth day it had calmed down so much that I try to introduce the new on. Bang - they start again with fighting mouth to mouth. I did the mistake to let the new one free in the morning. I succeeded to get up the new and placed it in the box again and released it on the evening after the light was out. In the morning - I aspect a very damaged clown. They was still fighting but in a semi aggressive way. Now a month later they exist together without other things than ritual fighting now and than. This video describe the introduction
Follow up video - after 17 days
Hope this give you some ideas and good luck
Sincerely Lasse