Right, it has to fit under the seat in front of you and not stick out in your personal foot space. I find that I can put my backpack or computer case in front of the aisle seat with foot room, but I can't fit it in front of the middle seat with foot room. Go figure. Personal carry-on is a pocketbook, small computer case, small backpack, briefcase, etc.
Those sound like the carry-on (stowed overhead) measurements, not the personal item ones.
As others have said, the personal item needs to fit completely under the seat in front of you, including any straps, handles, wheels, etc. I have a rolling bag that I ordered from QVC (.com, search for Travelon underseat or under seat but don't buy it the price went WAY up ) that's semi-wedge shaped, specifically designed to fit under the seat... just not the middle seat, as shoes99 knows .
I think ebags has something similar. It holds enough to get me through a night and day at my destination.