The problem with Apollonius is that, unlike Jesus, for whom we have at least five eye-witness testimonies (Matthew, Mark, John, Peter and James) we have no contemporary accounts of Apollonius at all. Our only witness to Apollonius is a third century writing by Philostratus who lived about one hundred and fifty years later. Besides, the oldest manuscripts of Philostratus are from the 12th century, making the reliability of his Life of Apollonius text a bit dubious.
Also, we have a refutation of Philostratus’ work by a Eusebius who may be Eusebius of Caesarea. Eusebius tells us that Philostratus’ work was fictionalized. Commentators tend to agree that Philostratus’ work was intended to be fictionalized from the beginning. In other words, Philostratus was purposefully mythologizing an actual person–the sage Apollonius. That contemporaries claimed miracles of Apollonius of Tyana is not at all certain.
This, of course, is the opposite of the case with Jesus. Contemporaries such as Matthew and John, as well as very careful historians such as Luke report that there were hundreds of public miracles, and that these signs and wonders were believed in by contemporaries in the regions where Jesus lived, both during his life and immediately after his life. I would say that there is no doubt that contemporaries of Jesus reported his miracles and this was believed by multitudes at that time. Otherwise we simply cannot explain the evolution of Christianity, which is a matter of fact.
Here is my take on the Apollonius story. He was almost certainly an actual person. He surely was a teacher who gained at least some following as a philosopher and sage during his lifetime. More than one hundred years later, a Greek author used the facts about his life to create a myth of Apollonius, including fables about his working of miracles and casting out demons, which was later used by the enemies of Christianity as a polemic against belief in Jesus as a unique religious leader. Given what happened to belief in Jesus of Nazareth, which is that Christianity eventually subsumed the Roman empire, it is clear what the conclusion of contemporaries of Philostratus was with regard to the Jesus vs Apollonius debate!
Here is the bottom line, I believe that you have not provided any evidence of sufficient strength that I feel the need to respond to the claim that Apollonius of Tyana did indeed cast out demons.
PS Please do not take this letter as being sent in an argumentative spirit. I am enjoying the interchange and hope you take this in the spirit of fun, not of a debate.