I'm not sure what it means for a layout page to "pick up" a stylesheet. So I'm going to assume that you mean that when the result of all the Spring and Tiles business appears in your browser, it isn't styled according to the stylesheet you expected to be used. I'm also going to assume that the HTML which you see in the browser does actually contain a reference to that stylesheet.
Now remember that it's the browser that styles the HTML, not Spring or Tiles or
JSP or anything on the server. And the browser has no idea what ran on the back end, all it knows is that it was given some HTML to work with.
So there are two possibilities: the reference to the stylesheet isn't correct, or it doesn't work. If you think you know the absolute URL of the stylesheet, you can type or paste that URL into your browser's address bar and see what comes back. If you do see a stylesheet when you do that, then that means the reference to the stylesheet in the HTML doesn't resolve to that absolute URL. Anyway that's the sort of
testing you need to do.