Data mapping actions don't execute when only sender signs -- Adobe Sign for Salesforce

I'm using Adobe Sign - Enterprise with Adobe Sign for Salesforce. I have a Data Mapping configured to update fields on the starting record when the document is sent for signature and update other fields when the document is signed. That Data Mapping is used by two Agreement Templates.

The first Agreement Template emails the document to several recipients for signature. The Data Mapping actions work as expected in that case.

The second Agreement Template uses Only Sender Signs. When using this template, none of the Data Mapping actions run. What's going on? How can I get this to work?