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.
There are numerous ways to export a group of pictures selected in Shotwell.
The file pane at the left hand side of the application window is a virtual library with a directory structure and folder names that do not map directly to the system's file directories. This can throw you off if you're coming from windows because the photo managers I've used there display a file directory identical to the system file directory, so you can drag and drop pictures to move the files around.
With Shotwell it's a bit more involved; Here's how to do it:
First create the group of pictures you wish to move about your file system -- here is a short, screenshot-laden tutorial for two ways of doing that: http://www.linuceum.com/Desktop/Shotwell.php -- but to make things flow, I'll add a method not mentioned in the linked tutorial: flags.
Navigate through your Shotwell directories, and flag the photos you want to include in the group of pictures you wish to move. Do this by right clicking the thumbnail, and selecting 'flag' from the right-click menu.
In the file pane towards the top you will see a directory named "flagged." Click on that directory, and all the photos you've flagged will display in the viewing pane. Select all the photos--control A--and click on the 'file' menu at the top of left of the screen. Select Export...and a dialog will pop up, which ends with the file manager's file choosing screen, where you can choose or create the directory to where you wish to move the selected photos. That's it.
I should note that you aren't actually moving the photos. You are but creating copies of them.
Best Answer
The simplest way to achieve this is with tags, not events. The short answer is to manually import folder-by-folder, and tag each batch of imports.
The first decision you have to make is whether to preserve your directory structure, and keep pictures in folders like you have them now. Shotwell defaults to a date directory structure, you have an event structure.
If you don't care, have all the photos outside /Pictures, and import one folder at a time using File/Import from folder... . Tag each batch as you go. All your photos will be reorganized in /Pictures based on dates.
If you want to keep the event structure, make sure to un-check the 'Watch library directory for new files' in Edit/Preferences/Library. Move all the folders with photos into /Pictures. Then import one at at a time, again tagging each batch of imports as you go. You will have to keep maintaining the library from then on, manually importing photos.