I’ve verified the plugin and it does try to set the correct response header on all sitemaps. It seems something on your server changes the response header afterwards to the wrong content type.
Also, headers seem to be completely different when I request /sitemap-posttype-page.xml with or without a random query strong like /sitemap-posttype-page.xml?nocache123 …
Are you using any kind of caching mechanism? Either a WordPress plugin or a server side caching solution?
I fear it’s only there that this can be fixed.
That said, it might not be very problematic. Have you submitted your sitemap index in Google Search Console? Have you seen errors reported? If not, you can decide to just leave it like this…