I recently had some issues logging into our netscaler appliances after a java update and decided to fix the issue instead of rolling back Java (frankly I am weary of Java and hope that Citrix wakes up and makes the admin HTML5 and ditches Java completely)
Simply add the sites to the exception list (use the management IP, and make sure to manage using HTTPS. ) under the security tab.
Hopefully the next upgrade will not require any new steps.
On a related note, i have been using a single browser (Google Chrome) to manage my netscaler appliances and i have not run across any issues that required another browser.