Hi and welcome to the Chiari forum.
No, a herniation of the cerebral tonsils is not Chiari....a malformation of the skull is Chiari, which makes the area too small to hold all of the brain and this is why part of it herniates. It is possible to have a herniation due to injury or another condition like IIH that can cause the tonsils to herniate.
That said, the symptoms are the same and many times treatment is the same.....
Many with Chiari do have a Tarlov cyst....and it appears there is some connection....but not sure if there is a study to show this.
Did you have a trauma to the head or neck?
It is possible that the radiologist is not knowledgeable on how to classify Chiari....so it is something a true Chiari specialist will have to answer for you.