The problem is that Shotwell will only copy the photos if they are located outside your XDG Pictures directory (usually ~/Pictures). If they are located inside your Pictures directory, Shotwell does not copy or reorganize them. (It's a tough call, but there are a lot of people out there who absolutely, positively do NOT want us to move their photos because they've gone to a great deal of trouble to organize them in the first place.)
From reading the comments to your question, it looks like you hit on a workaround: import all the photos from a folder outside of Pictures and choose copy. Unfortunately this means removing all the photos from Shotwell and re-importing them, meaning you lose all changes you've made to them (edits, tags, etc.)
We do have a ticket for exactly what you're looking for: http://redmine.yorba.org/issues/2170 No idea when/if it'll be ready, but we'd like to offer it.