The domain alias is not the problem.
With Google the user account alias is the problem.
How Google choose to DKIM sign or not
For Google to add the DKIM signature the username must be one of the Google account aliases.
Say you have DomainA.com(primary) and DomainB.com(alias)
Your google account is my@DomainA.com
DKIM signature will be set when sending from ...