After seeing your table setup, there’s a better way - use a de-reference to pull the signature from the ref column.
In the app formula for the actual signature field, use the following formula:
[Tabatha Linked Signature].[Signature]
That tells the system: “Look at the [Tabatha Linked Signature] column, we have selected a reference; from that reference we want the Signature value”
Using this setup will cause the signature to immediately populate when the signature reference is selected.
In regards to why setting this up as an action doesn’t work… that is strange, and I’m not sure why.