Usually that is handled by redirects on your old site. The how depends on what you use as a web server. That may give you a more granular way to approach this.
The other alternative is to point your “old” domain to your Webflow hosting same site plan. Any domains that are not the primary redirect by default. You can also add redirect rules for pages that may have moved.
I just watched the video you sent. So if I add the old domain to my custom domains under “hosting” and then make my new domain default, the old domain will redirect to the new one?