I got an email about a similar offer. I believe the previous offers were Hearst magazines and this one is with Meredith (Family Circle, Good Housekeeping, etc.). The offer this time is
Subscribe to select magazines and get a $5 gift card. Terms & conditions are
here. I don't see anything in this one about having to have gotten the email, but it does say you have to remain a subscriber through two billing cycles to get the $5 gift card (about 45 days).