The mod_autoindex.c module is part of the Apache HTTPD server, not the Apache Tomcat server. The clues are in its name. First, and foremost ".c" means C programming language, not
Java, and Tomcat, unlike Apache HTTP (more commonly known as simple "Apache"), is all Java.
If that wasn't clue enough. Anything named "mod_something" is almost certainly an Apache module.
Tomcat will index any directory within a webapp providing that there's nothing defined in web.xml that maps to the equivalent relative pathname. And, of course, providing that Tomcat has read-access rights to that directory. Although for directories within a WAR, that should always be the case.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.