Your code will work on those browsers that support it. And it won't on those that don't.
There is no standard/correct.
Overflow scrolling provides a barely adequate solution, IMO. It typically doesn't provide "native"-like scrollbar, for example. It's very dependent on browser implementation.
There are plugins for dealing with this in a cross-browser manner. Check out my own jquery.mobile.iscrollview or FT Scroller.