Add email address alias - proxyAddress attribute empty in on-premise AD

I have a client who uses DirSync and does not have an Exchange server on premise. During the initial deployment, we added the users' primary email addresses to the "mail" field in the AD user account properties which populated the "mail" attribute for the user in ADSI.

Now they would like to add an email address alias to an existing account. When I load up ADSI, the proxyAddress attribute for all users is empty. In the proxyAddress attribute field, I attempted adding the user's primary email address as STMP:email@domain.com and adding the alias as smtp:email@domain.com and then forcing a DirSync. However, the changes never sync'd and populated to the O365 user. I cannot add the alias via the web portal or O365 PowerShell due to the use of DirSync (gives me the out of write scope error).

What is the work around for this? How can I add an email address alias to an existing user?

Thanks