Directly after both type - manual, or via the Atlassian marketplace installation of the add-on you can spot additional element present in Jira under "Manage apps" (1) tab named "Contacts Audit Log":
As a typical log, it lists actions that happened in time with which Contacts Manager add-on has been involved. An example of it, in regards to new company creation is presented below:
All of the above is visible only to the Jira system administrator. To get a chance to find more possibilities offered by "Contacts Audit Log" check here.
To use Contacts Manager to added new entries, of course there's no need to have the highest rank of Jira administration. Any user within particular project, who has been granted with project administrator role can also spot additional element named "Contacts" (1), after proper project has been accessed:
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:
At current version you can sort only "Company name" (5) and “From project” (7) columns.
“Search” (2) - filter which allows searching needful contacts from the list.
“Clear” (3) - used for clearing the “Search” field.
“Export to CSV” (4) - with this option you can export list of contacts with all information to CSV file. Contacts chosen to export is based on “Search” filter, so if it is empty, all contacts will be exported.
Description (6) - contains nothing more than descriptive information in regards to company (i.e. scope of operations/services offered) placed during creation of new contact.
Next to it, "From Project" (7) informs in which project, an entry containing company's name has been created, thus giving a chance to quickly associate its operational area.
"Members" (8) presents in a numeric form how many people have been added to listed company, presenting potentially how big such entity is.
"Actions" (9) menu contains three options to chose from: "Edit" (10), Edit Members" (11) and "Delete" (12). Full description of its possibilities is described on a dedicated page.