Usually, if I want to check for some attribute of the post I'm about to publish, I will check like this:
$post_title = $_POST['post_title'];
post_title is the name of the title field in the edit window.
I thought I'd apply the same logic to the taxonomy meta box.
$formats = $_POST['tax_input[formats]'];
Essentially, I'm trying to check if a specific taxonomy term is being selected when I publish a post.