It may depend on the wording of the ad you responded to.

Originally the website said the free 1-4 was only for persons not already holding the Signature Premier card. Based on that, I got the free 1-4 certificate because of converting the regular Signature VISA to the Premier Signature VISA.

More recently, however, the site says the initial free 1-4 was for persons not already holding the Signature VISA (see footnote 3 on this site), so on that premise you wouldn't get the initial 1-4 for converting.