Many things can cause programs to automatically to launch as I'm sure you know. Some of the top contenders:
- Registry keys
- "Startup" folder
- Java trying to open a webpage
- System processes
- The list goes on...
My first suggestion would be to look into your registry keys (if possible, this may be locked) and see if anything calls Internet Explorer. Alternatively, you could boot into Ubuntu and manually delete Internet Explorer from the machines, but this is highly depreciated. Then, check if anything in your program could potentially use Internet Explorer (e.g. fetching data from a web page, APIs, etc.), Java has a tendency for causing strange issues such as this. If all else fails, you could convince someone to allow you to disable Internet Explorer.
Wish you the best of luck. ~Tsuser