This is a jxbrowser thing not really Ignition…
Check out https://jxbrowser-support.teamdev.com/docs/guides/chromium.html
It looks like you should be able to supply some additional jvm params in your launcher to change the dir according to the docs. The IA people can prob chime in if this should work or not.
-Djxbrowser.chromium.dir="Users/Me/.jxbrowser"