Why does URL Rewrite only work in Default Web Site?

I have done a fresh IIS 7.5 installation on my Windows 7 machine, and then I created a new website with its own ApplicationPool. So in total there are two sites under 'Sites':

1. Default Web SIte (with DefaultAppPool application pool)
2. MyWebsite  (with MyWebsite application pool)

When I write create a new URL Rewrite rule in the MyWebsite site, the rule doesn't work. I get a 404.0 error.

If I make the exact same rule (dealing with MyWebsite URLs) but do it in the Default Web Site then it works fine - except for CSS and images dissapearing.

Do all URL Rewrite rules have to be defined in the Default Web Site site? If not, how do I make different URL Rewrite rules that work independently in each seperate Site?