Hi!
How did you create your blog page? Because when we set the blog page as a category page, the sidebar works fine. It seems you’ve created a page and then assigned the blog to it. We’ve put the blog category page instead of the page you’ve created, and the sidebar works fine on it. The way you’ve created it made it use primary sidebar only.
But when you’re setting up a blog category page, you’ve need to go to Menus and then choose from categories, what blog you want.