My iPad mini has also start acting like it is being remotely controlled. I've narrowed it down to it does it or it starts doing it while taking pictures. Once it even placed a bid on ebay and once it listed something on ebay. To make it stop while it is going crazy I have to hold down the power button until it shuts off or there is no telling what it will do. It's like someone is just randomly tapping all over my screen and I can't make it stop.
I'll reboot, shut it down, clear the memory (I like SYS-activity), and sometimes that will help (for an hour maybe) and sometimes it will not help. Sometimes after shutting it completely off and turning it back on it does it immediately.
I have no screen protector interfering with the screen. It seems like it started happening right after the update to OS 9.3.1.
It does it whether I am taking pictures through the camera itself or through an app (like ebay). It's getting dangerous to take pictures because I can't control it once it goes crazy and I could bid a million dollars on something on ebay if I don't shut it down fast enough.
PS - I do not have multitasking gestures on.