I used CBT for depression, not autism. After I corrected distorted beliefs about myself, my depression went away. After I corrected distorted beliefs about other people, my social anxiety went away. Once that happened, my chronic stress (that I wasn't sure I had) went away and I unexpectedly found myself suddenly able to understand people to the point where I don't really have any social impairments anymore. It wasn't my intention, it just happened after correcting the distorted beliefs that made me depressed and anxious.
The traits and characteristic common in autism that about 1 in 10 people have are part of the broader autism phenotype. Most people with it live normal lives other than being a little odd and having a few problems due to neurological differences. Only about 1 in 5 end up with ASD. In my case (can't speak for anyone else), the additional problems I had were obviously psychological and not a part of who I am (since CBT won't make autistic traits or anything genetic go away). However, the research supports my claim. Studies estimate that 12% to 85% with ASD suffer from depression and/or anxiety. Why such a wide range? Because there's such a huge overlap in symptoms (most ASD symptoms also occur in non-autistic people with depression and anxiety) that researchers can't tell whether those symptoms are part of autism/genetic or secondary to it (depression/anxiety).