My problem explained in one picture: http://i.imgur.com/WY2UOyq.jpg
Top: Default Visual Studio settings - shows modifications in current session, and shows a different color depending on whether the modifications have been saved.
Middle: VisualSVN (plugin) that compares changes with SVN instead of per session modifications.
Bottom: Rider - no indication whatsoever that the lines have been modified.
Ideally, I would like Rider to behave similar to VisualSVN, since it also allows you to do things like reverting a code block to working copy.