I think it's a partnership. The therapist knows ABA, but you know your child. It has to be a conversation and a collaboration to make your child comfortable and responsive to it.
We are new to ABA but I think the therapist is. They are the ones with the individual goals, data sheets and timers. I work with my son on the tasks too, but when the therapist is there, they take the lead. Unless I have an issue with what they are doing. Then I step in.