No idea how you implemented your nginx script, but I know our network guy uses HAProxy and we run several WebApps on the same server without any issues in a folder structure like this, each with their own www (so js/css/font/...) folders.
/root/myapp1/myapp1.jar ON PORT 51042
/root/myapp1/copymewithjar.needs
/root/myapp1/www
/root/myapp2/myapp2.jar ON PORT 51043
/root/myapp2/copymewithjar.needs
/root/myapp2/www
/root/myapp3/myapp3.jar ON PORT 51044
/root/myapp3/copymewithjar.needs
/root/myapp3/www
Alwaysbusy