I figured it out. The issue was on the on-premise Exchange server. When an email would come in with <alias>@ssss .com the on-prem exchange server would see it as authoritative for that domain, as is should, and then attempt to route the email locally to the user. But the user isn't local anymore, it is on Exchange Online.
I edited the users within the on-premise exchange, clicked on Email Address and changed the Set as Remote Routing Address to the Exchange Online email address <alias>@<tenant>.mail.onmicrosoft.com.
Once that was done, the on premise exchange server started using the send connector created by the wizard and email began flowing.