Sounds like you're using cookies to maintain the sessions. When you open a new browser window, using the same browser, it will just overwrite the original cookie.
I usually allow the user to allow a cookie to be set, or not to use cookies. When they login, a radio button value of yes or no (1/0,true/false) is passed with their login info. If they opt to use cookies, a cookie is set. If they don't want to use cookies, then cookies must be turned off before calling session_start(); this will automatically append the session ID name = session id to all links on the page.
ini_set('session.use_cookies',FALSE);
session_start();
The session code is in 1 file which gets included in each of the other pages.
After login, I check to see if a cookie is set. If no, it will call ini_set again before calling session_start.