Yeah. That happened to me last year. A doe came down the hill and spote my set-up - a Jake and a hen. It was way cool. She came forward, then walked backwards a few paces. She snorted a few times. Then she came right in and began sniffing them. She never saw me and I don't think she scented me either. It was like she was coming down the deer trail and saw turkeys but there was something not quite right about these turkeys. It was pretty entertaining.
As far as chasing turkeys, far be it for me to understand what an animal like a deer is doing but, it sounds like they are playing, having fun. At the birds expense. Pretty cool whatever their motive.