Yes, they use the math to put the snippets in or out, and some programs have better math than others, and yes the technology is getting better, but it still has its limitations.
I don't doubt that some day it will improve to the point where transposing any audio file will be good enough not to be detectable by the human ear. But that day isn't here yet.
Some sounds transpose better than others, and what transposes well on one app might be different on another that uses a different mathematical model.
But how soon that future is going to get here is beyond my prediction powers. And when it does, you won't be able to hear if the 'singer' is using auto-tune or not

Bob