I spent a long while figuring out how to get custom page titles to work on taxonomy term pages.
* I have a Vocabulary 'Category' for which I set a default pattern: [term:name] | [site:name]
* Checked 'Show field'
* Visited the term form for a term in 'Category' - the term is 'teacher'
* Added custom page title 'mytitle'
* Viewed the term page
* Could not see 'mytitle' as page title. Instead it was: teacher | my site name
Try as I did, I could not figure out why my custom page title for that particular term would not appear.
I first thought it was because I was using a view to display the term page.
However on further introspection I found that hook_page_title_alter() was called only if the default pattern for the Vocabulary was: [current-page:page-title] | [site:name]
Only when token_replace on 'current-page:page-title' is run, would hook_page_title_alter() run, and correspondingly taxonomy_page_title_alter() would get called to set the title to the $term_title.
I would presume this is a bug rather than missing documentation. But if there are gaps in my understanding, please convert this to a documentation request.