How much are sound designers expected to integrate this sort of thing?
That would depend on how much you want to make yourself more valuable to the industry.
If you learn the skills to be able to do that, not only will you be in more demand, but you'll be able to command a higher wage than someone who only creates the sound, expecting that someone else will take care of the integration.
Great response to a great question. I know that I am one of many who would like to try their hand and imrpove their skill at sound design/implementation. Plus, being in demand ain't half bad either. Are there any things that we can do, as upcoming sound musicians, to gain experience with that kind of thing? I looked up FMOD and had a brain aneurysm when I saw the prices. The closest I have gotten to sound implementation is RPG Maker, which isn't saying much.