Edit:

I'm asking this just to ensure that if I'm running an older version supplied by ubuntu(installed from through apt-get install), am I safe in terms of security & quality of software?

By default, now Ubuntu includes backports. Meaning? That security fixes are delivered to you fast and steady if they are fixed upstream. These add up to the fact that the security repository should be in your sources.list too. Hence, installing from repositories will keep your system security while you keep it updated.

Ubuntu by default checks for updates each ~24 hrs and install security upgrades immediately.

Do these software packages will be updated to a newer minor version later while I m sticking to a particular LTS version ?

Here your are contradicting yourself. You said that you don't have to stick with a particular version of Tomcat, yet you are fretting if a minor upgrade get released. LTS are for people that prefers stability over innovation. If you keep your system upgraded and follow the standard security methods, you will be fine.

But it is unclear that how ubuntu updates the tomcat because the minor version never changes, it always stays on tomcat 7.0.26 with ubuntu 12.04.. !?

If you check the package versions instead apt-cache policy tomcat7, you will notice that there the version change. You should also check the changelog and notice the precise-security updates. These packages gets installed in your system immediately they are available. The internal version of Tomcat will not change, since:

1. Ubuntu is applying a minor patch that solves an specific issue.


2. Features are not introduced in backports, only fixes.


3. As features are not introduced and some code depends of an specific version and down/up to work, these are not affected.