Using their website (that didn't work for me in Firefox but did in Chrome), you have to add the upgrade to your 'Passport' then click the yellow 'Email me my Passport' button. Your voucher comes as an email. Note that it is directly in the body of the email, not as an attachment.
I've printed the email to PDF to show you how it looks. I agree it's hardly the most professional rail document around! The boilerplate waffle that is printed on all vouchers through this website says you don't need the voucher anyway, you just show the voucher on your phone when you pay... Does this mean you need to exchange the voucher for a first class excess or supplement at a ticket office before boarding? It's not very clear.
Obviously you'd need to get your own voucher if you wanted to take advantage of the offer rather than using mine