When Twilio SendGrid receives your email request, we look at the domain used in the From (sender) email address, and attempt to match it to the domain set in Link Branding for your account. For example, a sending email address of example@mysite.com would match the Link Branding of url1234.mysite.com because they share the domain of "mysite.com".
When the From (sender) email address domain does not have Link Branding set up, Twilio SendGrid instead uses the default Link Branding, which is sendgrid.net. If you want emails to have a default Link Branding, you must flag one of your Link Brandings as Default.
Please note that while Domain Authentication and Link Branding are both applied based on the From (sender) email address used, they are controlled via different settings in your account.