Behavior of MMT Semi-Automatic Drives Corolla etc.

Hello, recently bought me a Toyota Corolla 1.4 Diesel with MMT automatic/tiptronic. The car is so perfect, but the transmission is annoying. The data: Built 2006, km 76000, 1st hand, checkbook, Toyota warranty! I have to say that I have been driving all kinds of automatic transmissions for 20 years, mostly full automatics but also automatics. The automatic circuit of the Toyota is very treacherous and imprecise. With strong acceleration and high speeds, the H switch by a few seconds! Also otherwise the Toyota does not switch precisely, i.e. often too late or sometimes delayed or too early. With manual operation, the behavior is flawless. Since I am not familiar with these gearboxes from Toyota, my questions: Is the behavior normal? Can you adjust the switching torque? Does this indicate a gear damage? Ciao Fred