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)
The fix I used was found in the JAVA control panel applet.
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.