Google Not Indexing Meta Tags

I installed All-in-One SEO Pack, and entered title and description meta tags for each page. When I look at the code in “view source” I see the tags appear correctly on each page.
However, Google won’t index these tags.
I tried submitting the site for indexing in Search Console, and waiting, but nothing changed.
My site’s pages still appear in Google’s search results with the wrong title and descriptions.
What can I do to fix this?

Also, when I use All-in-One SEO Pack, what should be in the <title> tag in my header.php file? Can Google index this tag instead of the All-in-One SEO Pack tag, even though I have “Rewrite Titles” enabled, and the correct tag appears in the source code?

Thank you!