Job Manager uses WordPress built-in capabilities for its menu protection:

Job Manager publish_posts
Settings manage_options
Add Job publish_posts
Jobs publish_posts
Applications read_private_pages
Emails read_private_pages
Interviews read_private_pages

You can use “Admin menu access” add-on to block for the role of this user the access to the unneeded menu items, which will become available for it with capabilities above together, like “Settings”.