When a review moves to the status of "awaiting signature," it indicates that the review is complete and signatures are pending. The admin may or may not have generated the PDF at this point. The admin must generate the PDF for the learner to be prompted to sign it. If the PDF is not generated, the learner will not see the "signature required" status in the "requires attention" drilldown on their dashboard.
Clicking the Finish button does not automatically add the tutor/admin's signature. The tutor/admin must apply their signature before generating the PDF. If they generate the PDF without applying signatures, they can still sign later.