I really don't understand the confusion here. Never understood the confusion. They said it so many times in regard to what happen. . They were very direct with it.
Voq's body was altered. His bones were sawed down, even refilled to reduce his height, etc. Extra organs that Klingons have were removed and maybe replaced with that of the real Tyler's. Physically Voq was made to appear and pass for human under normal medical scans. That's why the changes weren't detected and the scaring was reasoned to be a result of the physical torture he was said to have gone under. It was that operation the Ash personality took for torture. Then the real Ash Tyler's personality (he was a real person. The back story he gave was real and did check out) was grafted on top of Voq's. The end result Voq was a sleeper agent waiting to be woken up but the change was to good and as a result the Ash Tyler personality was far to strong and wasn't letting go. It was strong enough to do that because he had fallen in love with Burnham and that bond was strong.
Each time they talk about it they go into more detail each time but it doesn't contradict. The only question I could understand someone having is how they grafted the personality. For that I just fall back on "Star Trek future science".
I don't know if people are looking for more or feel it has to be more complicated then that but I thought the show was very clear as to how it was actually done. They repeated a few times just in case people missed it.
