The tab doesn't display the articles, but displays a list of articles. It will only display the articles that the user is the creator of. When you click the article title it'll take you to the articles display.

When I click the article title, it will bring me to the home page.

Create a Joomla menu item to the category of the article. My guess is it's using the Itemid of the home page as the article is being displayed there. CB doesn't generate the article URLs, it calls Joomlas own content component API to generate them.

I like to let the user modify the articles on the front-end.

That's not what CB Articles does. It's strictly to display on profile in a tab a list of articles the user is the creator of. To create new articles you need to use the Submit Article page provided by Joomla or use CB Blogs.

Members cannot create a joomla menu from front-end. If every members need to create a menu every time when they create an article, it doesn't make sense.
In that case, members cannot see what they wrote on it after they create an article.
I cannot create menus on the back-end every time when members create an article.

They don't need to. A hidden menu item to the category would work fine. This is out of our hands so I don't know what to tell you. That's how Joomla is designed. Joomla links need an Itemid when using SEF. Joomla will add the Itemid for the closest matched content menu item to the URL when ran through the content router API. So by creating a category menu item it'll use that menu item for its Itemid for example.

I want to let my members create an article from front-end and check the article list on their profile screen using CB Article. Then when they click the article on the list, I want to make them be able to review their article and modify before publishing.
After they submit the article, I will review it and approve before showing to the public.
I don't want to use blogs for this function.

That's exactly what CB Blogs can provide. CB Articles is display only. It does not and will not have creation functionality. If you want them to be able to create articles without using CB Blogs you need to use the Joomla Submit Article page by creating a menu item for it. Your alternative is to look into K2 or some other content extension and use its article submit functionality.