International sitemaps with hreflang and search console

I'm using shopify's 'local domains' feature, which essentially gives me several domains as hreflang tags with the relevant ' hreflang tag on each page showing the various language/country options. But I've noticed that the sitemaps generated don't include alternate links, but are available at every domain. So for example www.website.com.au/sitemap.xml gives australian links while www.website.co.nz/sitemap.xml gives new zealand links.

My questions are:

1)Should the sitemaps themselves include the alternate links for each page? This page from google suggests it should but I can't tell if that's in place of having it defined as hreflang tags on the page itself.

2) Should I instead create a second Google Search Console account for the alternative domain and submit the alternate sitemap there or is there a way to do it within the one account?

Thanks!