I had a case where an extra tab was necessary on the user pages. This snippets show you how to do it.

I had to provide an extra controller for an SSO log in via OpenID connect. I created an extra controller and added a file named my_module.links.task.yml to my custom module. Use the following yaml structure and tweak it to your purposes. Clear caches and you now will see "Log in - Register - Password reset - SSO login" as tabs. 

my_module.ssologin:
  route_name: route_name_of_controller
  base_route: user.page
  title: 'SSO login'
  weight: 20