A subject of another thread. How many of us have exited our Prius and looked through the window and wondered why our display was still on.
Not exactly the same thing, but something similar happened to me, or rather, I did to myself. I stopped by a local corner store to grab a drink, got out and forgot to engage the e-brake or keep it in gear (standard transmission). I walked up to the door and was about to enter and out of the corner of my eye I saw this blue blob heading toward the street! It was my '06 Spectra!!! I ran after it, got into the driver's seat and hit the brakes just as the rear end was going into the street! Luckily, it was late and there were no other cars around. Funny thing is, when I pulled back up to the parking spot, these kids that were standing around in front of the store, talking among themselves didn't even notice what happened! Phew!
My 2012 Pri 4 always auto-parks when I hit the power button with the brake depressed. I only use the Park when I'm running into the house/school with the engine running. I don't always use the parking brake, unless the surface is on a slope, since I hate it settling against the gears. Could it be that the brake pedal isn't pushed in enough when you power down? Maybe I'll remember to try that. Otherwise, something is wrong with the Prius.
My problem is that I have become so used to hitting the power button to park and shut off the Prius that, on more than one occasion, I've neglected to shift my roommate's Outback into Park. I'll just hit the start/stop button and exit like I do with my car. Thankfully, it beeps quite loudly at me that I haven't done everything I should prior to exiting.
Prius does not have the little drum in the center of the rear disk. The parking brake cable just attaches to the rear calipers.
I never use the parking brake when I park in city streets at work - the few inches of movement in the parking pawl helps when people nudge you when parking.