Relevant Product: Exclaimer Cloud - Signatures for G Suite
You have granted users permission to send email from a group's email address by following the instructions from Send emails from a different address or alias, however, the sender's signature is applied to the email.
When an email is sent as a group in Gmail, the Return-Path header is populated with the primary SMTP email address of the user sending the email as the group.
When Exclaimer Cloud processes emails, the user whose signature should be applied to the email is determined by the email address populated in the Return-Path header. So, the signature of the user who sent the email will always be applied when the email is sent from a group's email address.