I've run into the same problem, and written the plug-in author:
Hello, I've run into a problem it looks like a few other users have as well:
Specifically, here is the issue:
I have created a privately hosted blog with a static Page named "Home". I have created a second static Page named "Blog". In the WordPress Settings - Reading section I have set "Front page" to "Home" and the "Posts page" to "Blog". I don't think this is especially unusual.
By default, without AiOSEO enabled, both the Home page and Blog page will have titles of just "Blogname". Unfortunately, AiOSEO does this as well: any changes made in the AIOSEO Options page to the "Home Title:" section appear on BOTH the "Home" page (the default static page that appears when the site loads), as well as the "Blog" page (the one where posts appear).
I have tried adding a custom title to both pages in the AiOSEO section of the respective pages where you can specify a different title. This field works correctly for other static pages, overwriting the default title, but not these two pages.
To address this problem I would like to make two suggestions:
1. AIOSEO should take into account when the user has a separate home/main page on the site, and posts page, and allow for creating different titles and tags for each.
2. AIOSEO should allow title/description/keywords entered into the Page itself to supersede defaults in the AIOSEO settings page.