I don't use a expander die unless I'm necking up brass (from 6BR to 30BR, for example). In that case, you're going to have to fire form to get it just right anyhow, so I don't worry about runout. My Sinclair expander is really old, but it just holds the mandrel - the case is unsupported.
When neck turning an off the shelf caliber, I take a brand new case and turn it right out of the box. The mandrel on the turner (which might be a slightly different size than the one for the expander die) should be a tight slip fit. I do this by hand, although I don't think that matters. Are you saying you cannot turn the brass without first expanding it?
In any case, I wouldn't worry about runout until the brass has been fired, especially if your'e dicking around with necking up/down. What you should see is a consistent neck thickness all the way around the neck. Within a tenth or two (you'll need a tube mic to measure this accurately).