Asda Mobile is sending new SIM cards out in the same packaging to existing customers (who're simply transferring between EE's network and Vodafone's) as they do to new customers (who're joining Asda Mobile from another service provider). That's causing confusion because that packaging refers to getting a PAC code from a previous provider, which existing users simply don't need.
If you've not already got a new SIM, log into your Asda Mobile account to order one.
If you've got a new SIM, log into your account and follow the instructions there to schedule your port-in start date. Leave your old SIM in your phone until when, on the day after the date you've specified, the signal vanishes. Then replace your old SIM with your new one.
You'll also need to log into your account (or call 2732) to re-order any recurring bundle you might have. (That's because the bundle packages are changing, in your favour, when Asda switch to EE's service). If you call 2732, you'll hear a message telling you that they're experiencing heavy call volumes and suggesting that you go online. Ignore that and keep pressing button until you reach the option to speak to an operator. The wait is actually quite a short one anyway.