I highly recommend discussion of the development of the ansible in Ursula K. Le Guin's The Disposessed as well, although she makes it pretty clear that there's a different theoretical basis for it ("simultaneity theory") than the one Card uses.
Does it address what would happen if I, relative to your reference frame, got in my spaceship, accelerated to .5c and tried to talk to you over my ansible? From my perspective, you're traveling slowly in time, but from your perspective, I'm traveling slowly in time, so who's voice would sound slowed down?
I don't remember if the interface was realtime or async off the top of my head, but it would strike me as uncharacteristic of her (and strange in the context of the plot) to not take that into account.
I'm not even sure if the ansible interface is actually described anywhere in that book....