That is not how Dreamweaver is supposed to act. You can check the preview setting by going to the Edit menu, Click on Preferences, then click on Preview in Browser in the left side Catagory list. You should see "iexplore F12" in the window. You can change this by clicking on the Edit button.
One thing though, if your site uses absolute links then those links will go to the live site. You need to use relative links for proper testing on your local machine. Here are examples:
absolute link: http://www.howtogurus.com/support.html
relative link: ../support.html or just support.html, depends on where the file is relative to the page linking to it.
Basically if your links have http://www.whatever.com (your web site address) included in them then those links will go to that live page. Also if your opening page automatically goes to your live site through a forwarding absolute link (like you have a splash page or something) then you will see the live site and not your testing site.
My guess is that you have absolute links on your testing site. But even with absolute links it should show the first page you open on your local machine since you are not going to that by an absolute link, but are opening it directly.
