In the US (at least in the Boston area) it's another matter, and it's almost as if people just don't know what they're doing, and after doing my driving test here I'd believe it. :)
If you want to exit after 90 degrees, outer lane. If you want to exit after 180 degrees (straight through), either lane. If you want to exit after 270 degress, inner lane at first, then start indicating you are exiting, perhaps moving to outer lane before exit. The latter sounds confusing, in practice it isn't, mainly because other people will be expecting it.
My confusion about the multi-lane roundabout mostly stems from the scenario where two cars, entering from streets 90* in the direction of the flow apart, both want to go straight through. If the one entering 'upstream' takes the inner lane and the one 'downstream' takes the outer lane, it would seem that in some timing conditions you'd get a collision situation when the inner lane car tries to exit but must cross the outer lane to do so. Is this a practical concern? Is there a universal set order of precedence for this case, e.g. inner lane always yields if necessary?
In places I've driven where there might be confusion, they mark the lanes with arrows to show which ones are exiting and when.
They work pretty seamlessly in my experience. You only have to look one way (upstream), instead of two, to judge whether to enter the intersection, and you don't have the time-waste of traffic lights.