To reproduce 1) Add different products to cart 2) Go to checkout [just before confirming] 3) Now from cart drop down remove a product. Changes will not get reflected in cart. Ideally if you are in these pages if a change happens e from the drop down cart a force refresh might be a quick fix. I think this is a bug.
I agree with you that it looks like a bug and it should refresh the page but at the same time the idea of the Flyout cart is to work with Ajax and not to refresh the page.
If we make it to refresh the page then some people may complain as they like the current behavior that does not refresh it.
Let's see what the others think about it and we might change this to trigger a page refresh when items are removed from the Flyout cart.