We use JavaScript to render the SEO and Readability Scores. We have a guide that helps users better integrate their plugins here: https://github.com/Yoast/YoastSEO.js/blob/master/README.md

However, some plugins such as WordPress import ones may not be able to integrate well or other plugins may not be able to integrate at all.

For example, users who create import scripts to automatically populate _yoast_wpseo_metadesc, _yoast_wpseo_focuskw may not be able to recalculate the SEO/Readability ratings without lots of hacking.

We may wish to move part of the logic to the server side or add additional hooks/filters etc. to make it easier for other plugins to tap into the JavaScript.

See also: https://wordpress.org/support/topic/programmatically-update-scores/