In a web-application implemented in java using JSP and Servlets; if I store information in the user session, this information is shared from all the tabs from the same brows
You can use HTML5 SessionStorage (window.sessionStorage). You will generate a random id and save in session Storage per Browser Tab. Then each browser tab has his own Id.
Data stored using sessionStorage do not persist across browser tabs, even if two tabs both contain webpages from the same domain origin. In other words, data inside sessionStorage is confined to not just the domain and directory of the invoking page, but the browser tab in which the page is contained in. Contrast that to session cookies, which do persist data from tab to tab.