Archie,
If you're using J2EE session management, it isn't Coldfusion
that is or isn't handling it "correctly", it's JRun. All J2EE
servers handle this the same way. Sessions are tracked via cookie
unless cookies are disabled, then it falls back to URL rewriting,
but you need to make sure you tack it onto the end of all your
links, form posts, etc.
Because it uses a cookie to track sessions, the browser would
need to keep per-window-instance or per-tab-instance cookies rather
than application-wide cookies. My guess is when you open a new IE
instance from the Start menu, it starts with no transient cookies.
When you do File->New->Window, it inherits the transient
cookies of the parent Window. All other browsers all have shared
transient cookies across all instances and tabs.
As I already said, if you want per-window-instance or
per-tab-instance sessions, you need to track your sessions using
URL rewriting.