Regarding the browser cache, if you have any other browser session (with the same browser) open to any web site, your cache for Windchill is not cleared. So it will remember who you are and connect you immediately. You have to completely close all of the browser tabs and windows, to clear the session cache. Since Internet Explorer and FireFox do not share their caches, they are independent of one another.
Internet Explorer 8 has "New session" under the file menu that does the same thing as a completely different browser. But all tabs that are opened up in the same "session" will keep the cache alive.
Hope this helps.
Mark Plimley