There's no lock I'm aware of but we've ordered the tri-fold cargo liner which I suspect will help keep everything down. I suspect that in the interest of maximizing space and seat comfort they've made it such that the seat cushioning is actually slightly compressed when they're stowed. A little bit of cargo weight keeps them down but left on their own I've noticed they do stick up a bit. It's also a matter of balancing the mechanism that brings them out of the stowed position -- the salesman made a big deal of showing us how you could open it up with one finger (cause I need to do that all the time!)
Congrats on your new purchase and welcome!