How to set different logout times for roles?
We can achieve that using the Automated Logout module. combination of the Javascript Timer module.
Using the Automated Logout module we can set different timeouts for user roles and using Javascript Timer we can display remaining session time (countdown timer) for a logged in user.
Automated Logout

This module provides a site administrator the ability to log users out after a specified time of inactivity.
It is highly customizable and includes &quot;site policies&quot; by role to enforce logout.
Features

Different timeouts based on role
Disabling of timeouts based on role
Permission for users to set their own timeout
Includes some JS mechanisms to keep uses logged in even if multiple    tabs are open or if the user is working on a form for a long period
of time.
Includes developer hooks to allow users to remain logged in depending    on your own project specific requirements
Optional integration with Javascript Timer Timer