Dropbox created a duplicate of all files, with "._" in front of each file name

The ._ files are generated by the Macbook user's OS - used to store additional meta information about that file. Dropbox is not really creating them, they are simply being copied from the Macbook user's machine. These files are normally "hidden" and hopefully the "hidden" attribute is still intact so they can probably be hidden on the Windows machines as well.

More information:
Is there any way to prevent a Mac from creating dot underscore files?

I found this post a few weeks back when I was looking for information about sharing a Dropbox folder between Windows and macOS using Bootcamp. Since then I've done a fair bit of investigation, which I've written up here: http://www.dylanbeattie.net/2017/01/sharing-dropbox-folder-using-bootcamp.html

Short answer: they're not created by Dropbox, they're created by macOS if you're using a non-standard filesystem, which I suspect your macOS-using collaborator is doing. They're normally hidden files so you'll never seen them, but Dropbox picks them up and syncs them to any other devices - and in some cases they lose the hidden attribute. Rather than deleting them, you can set them to hidden on a Windows machine using this command:

C:\Users\me\Dropbox> for /r %1 in (._*) do attrib +h "%1"

That's saying 'find every file in this folder and subfolders whose names matches the pattern ._* (i.e. dot-underscore followed by anything), and set the Hidden attribute on that file to true'