Clarification when the module can be used

Let's clarify what you can do with this module and what can be done with Views by default.

1st level menu tab - only Views needed

Let's say you want to put a new tab to the user page. Actually, that would not be a 2nd level local task tab but a 1st level menu tab. For that you don't need this module as you can set it this way:

For a Page view set:
Path: /user/%user/content
Menu:
- Type: Menu tab
- Set Menu link title to "User's content" (or whatever else)
- Set weight
- and leave the rest of the settings as they are default

Also, under Advanced > Contextual filters, add Content: Authored by.

After cache clear you should see like that:

2nd level local task tab - can be added with this module

Now, if you would want 2nd level tabs under that "View" tab on the user page, then you create a Local task for example with "Recent" and "All content", then you can do it with this module. The result would look like this:

And for this example, I created 2 separate views with URLs:
- user/%user/recent
- user/%user/all

I added a Menu: Tab where
- I enabled the "Local task only" option
- I set "Recent" (and in the other view "All content") as Menu link title and Local task link title
- now, the tricky parent route option: the user page is not a view but the User entity's canonical page, so I installed devel module which can search for route names at /devel/routes:

As you can see, according to the devel module, I need to set "entity.user.canonical" as a "Custom" Local task custom parent route name.

If you don't want to install the devel module and you can access the database via phpMyAdmin, CLI or another tool, you can query the router table for the same thing, too:

And saving the views and clearing the cache resulted showing the 2nd level tabs. Also, you need to remember that 2nd level tabs are not displayed until there's at least 2 of them.