This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
Is the bean an instance variable in the servlet? If so, the servlet still has a reference to the first browser's associated session bean. And as multiple users share a servlet, the second browser could see that.
The stateless session bean itself should work as you describe if called properly.