Hi Bhagya,

In short, if the “Install delivery” option is used for installing the delivery, installer_delivery.xml is updated. 
If the “Install delivery and Reconfigure” option is used for installing the delivery, installer.xml is updated.
Please note that even when choosing the “Install delivery” option, depending on the delivery content (E.g. Update delivery, Middleware Server Patch), the installer will forcefully choose “Install delivery and Reconfigure” option.

Clarifying further, when starting the Installer, the installer.xml and the <instance>_configuration.xml will be loaded and values will be set in the installer.
These files will only be updated when running in "Reconfigure" mode (Install delivery & Reconfigure option).
When running in delivery mode (Install delivery option), installer_delivery.xml and <instance>_configuration_delivery.xml will be updated.
The reason of having different files for the different modes was to not change the basic configuration for the installation when deploying a delivery. 
A delivery could contain files to be imported, and the logic in the Installer gives you the default values of what should be imported, may be something that you do not have in your "configuration.xml". So, the Installer instead saves the values in its own "mode" file, to not interfere with the actual configuration. 
This is how it has been designed to work.

If the query is related to keeping track of installed deliveries, then I would suggest checking the module_tab table in the database or "Installed Components" window in IFS application as it has more information about the installed deliveries.

Best Regards,
Sasika