It doesn't mean the website is using the same certificate. One can include as many domains as they want in a certificate, but nothing stops them from using something else.
But it's probable that they have some certificate renewal script that has reloaded the certificate on their website, but the service that you're connecting to still has the old certificate loaded.
Edit: yep, see https://bgp.he.net/certs#_SearchTab%3Fq=api.xmpp.jp , it looks like they did a renewal recently, but probably haven't reloaded their cert. So it'd probably be fine to accept it, or just wait a bit for them to realize and reload.
I'll test your drugs for free!