What you're asking of a PTZ is for it to determine what kind of motion is sees, regular movement of the camera versus movement from some other source. Frankly, I don't think there's a PTZ on the market that can do that and, if there were, it would be priced well beyond what consumers would want to pay, probably even big, corporate, users and governmental agencies. That said, auto tracking can help somewhat but keep in mind PTZs generally have a fairly long focal length even when zoomed out which makes close up views problematic in many instances.
The problem with a PTZ is that it is fun to play with, but when needed it always seems to be looking in the wrong direction. Assuming you're talking about a decent PTZ the cost is in the $400 and up range. Two, or even three, fixed cameras would be much more reliable for either less or equivalent money.