For anyone wondering, this works even if you didn’t get the email (I’m not signed up for their email) or the offer/coupon showing in the app (mine had some other coupon). I signed up for Big Lots rewards a while ago, just haven’t really bought anything there yet until today.
There were also reports on blu-ray forum that you can sign up for Big Lots rewards even after the promo started, and then you can pick up your free blu-ray/dvd; however, I have not tried that, and I’m not sure anyone else has at blu-ray forum either.