Issue with Routing: My fault or Bug?

Your baseURL should not include "public" - that should be handled in your web server setup.
Your document root should be set to PROJECT_FOLDER/public.
Your baseURL would then be 'http://example.com'
And redirecting to '/manage' should go to the right place.

The way you have it configured, the browser thinks you are in '/public/manage/...', and redirecting to '/manage' is behaving as it should given this.