The admin and manager apps are two separate things. Here's a snapshot of a tomcat-users.xml file that works, try this:
<?xml version='1.0' encoding='utf-8'?>
<tomcat-users>
<role rolename="tomcat"/>
<role rolename="role1"/>
<role rolename="manager"/>
<user username="tomcat" password="tomcat" roles="tomcat"/>
<user username="both" password="tomcat" roles="tomcat,role1"/>
<user username="role1" password="tomcat" roles="role1"/>
<user username="USERNAME" password="PASSWORD" roles="manager,tomcat,role1"/>
</tomcat-users>
It works for me very well