After app installation you can spot additional element present in Jira under "Manage apps" (1) tab named "Contacts Audit Log":

It will lists actions related to Contacts Manager app. Here is an example after a new company creation:

Feature is visible only to the Jira Administrators. More about: Contacts Audit Log

To use Contacts Manager you need to add new companies. Users with project role Administrator are the one allowed to create new entries in ‘Contacts’ tab.

Upon accessing it, if there's an entry already present, added via "New contact (1) button, you should see a similar view, with list of all companies: