Sorry for the delayed response to this. Upon a good amount of research, I have determined that you are in fact the only manager to have won four trophies in one season! There have been a few close calls. Here is what I've found:
Manager rwystyrk of BC Hostivař was close in season 17. Rwystyrk won his league title, cup, and won the Europe Tournament as the NT coach of Česká Rep., but lost in the final 16 of B3.
Manager Mamba888 of Dionysus was close in season 22. Mamba888 won B3, his league title, and won Worlds as the NT coach of China, but was miraculously knocked out of the cup in the round of 512 in a crushing 129-70 loss to the 438th ranked team in China.
Manager Sister Niu of 猛牛 was the closest in season 25. Sister Niu won his league title, the cup, won the Asia Tournament as the NT coach of China, but lost 102-99 in the championship game of B3 to Młoty Stargard!
Managers that I have found that have won a league title, cup title, B3 title, and NT title:
Sahand of I Love Tehran - won America Championship with USA and Asia Championship with Iran
rwystyrk of BC Hostivař - won Europe Championship with Česká Rep.
Mamba888 of Dionysus - won Asia Championship and World Championship with China
LA-zajino of Nitra Corgons - won Europe Championship with Slovensko
I will also present a list of teams that may have accomplished getting all four trophies, but it cannot be determined since the teams went bot. These are all teams that have won a league title, cup, and B3, and have since went bot. To narrow this down and make this list seem more likely, I have only included teams who have had their country win a Continent Championship and/or World Championship during the time in which they were a manager.
Springlfield Drunkers of Italia
龙里农商银行 of China
KK Zvezda je zivo of Srbija
Topola Eagles of Srbija
I suppose to make this a "true" four trophy club, I would try to find managers that have won U21 championships as well. However, this exercise took way longer than I was expecting just for NT managers, so I don't think I'm going to get around to that.
Also, the winning championships in different continents record may be something I look up another time. But I am too worn out to do that right now.