Guys I think I found the problem.
I was getting this problem in Tomcat 5.5.28 also.
Reason :
In webapps/ROOT, we have a folder called admin. In this by default, we have a index.html file which gives the message 'Tomcat's administration web application is no longer installed by default. Download and install the "admin" package to use it. '.
This file is used to alert that the admin package should be installed but when you copy the admin package files, there is no instruction to remove this file.
The reason that this file opens up as default index page, when /admin is given in the url, is that the welcome file list contains index.html first and then index.jsp.
That's the reason for the admin page to come up when index.jsp is added to the url.
Solution : Remove /webapps/ROOT/admin/index.html file after admin package is installed to solve this issue.
Note : I noticed that this issue does not show up always.
Sorry for digging an old issue. All feedback is welcome.
'njoy
Rajiv