This plugin doesn’t hide menus on the frontend. If we’re talking about the admin dashboard, the jobs functionality there is more geared towards admins so you’d need to give the role additional permissions. Remember; job posters (employers) should be submitting jobs via the frontend job submission form.
Why couldn’t they get access first and then from wp-admin post a job?
They could, if you change the employer role permissions.
https://wordpress.org/plugins/user-role-editor/
Sure, but I thought it would be logical if this was assigned to the Employer user role by default.
No; if I did this then they could bypass the paid listing plugins (which work on the frontend).