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The Run action on web project opens a browser, which is expected. However, Redeploy also opens the browser, which is not what the user expects. Redeploy should only deploy the module and not open the brower. This is currently not specified well in the spec: http://web.netbeans.org/nonav/doc/webapp-project-ui-spec-promoe.html#Node_Web_Application should be described more clearly.
Let's consider it UI spec bug. The functional part is filed as issue 51599.
The Web Application UI spec has been updated to make it more clear, that the browser may pop up on Run action. But still the run/redeploy actions need to be specified more precisly. This is a task for the time between promo e and promo f.
Reassigning to Jano, who works on Java EE.
This old bug may not be relevant anymore. If you can still reproduce it in 8.2 development builds please reopen this issue. Thanks for your cooperation, NetBeans IDE 8.2 Release Boss