How to correctly use Certbot to update or change domains?

Did you add the second domain to the same VirtualHost in apache, or a new one?

Is the second domain actually redirecting, or not?

Yes. However, if you'll be doing this more than 20 times a week, keep an eye on the rate limits. Adding a domain to a certificate counts as issuing a new certificate containing both the old and new names, so it counts towards the rate limit for both (if they're different).