When I run yum install X, where X can be tomcat or any other package, whats the user and the permission on the packages it downloads ?
Do you mean for the dowloaded .rpm files?
If you use yum install somepackage the downloaded .rpm files will have root:root as owner and group and will be temporarily cached in folder /var/cache/yum/reponame/packages and permissions depend on the umask for root user, but default should be 0644.
For the files contained in those package (which will be put into place during .rpm installation) that solely depends on the definitions that are assigned when the .rpms are built via the
%files section in the .spec file used to build the package.
Can be queried for packages that are not installed via rpm -qpl ./package.rpm -v and for installed packages via omitting -p and the suffix .rpm, so e.g. rpm -ql package -v
