It’s not going to say anything about it in the shops. Once you signed up you have the promotion attached to your account. Once you make a purchase for $40+ it will credit to your account within a few days (I posted the “fine print” above for estimated payment timeframe and it’s on the Rakuten site). If you want to you can PM me the username you signed up with and I’ll screen shot you your name back from my account to show you’re signed up in the promotion
Edit: I tried to add a screenshot from the bottom the of initial sign up form you submitted but the image is coming up broken. It says in the terms:
"* To qualify for a Referral Sign-up Bonus, you must be a new member and place qualifying orders totaling a minimum of $40 within 90 days of becoming a member. You must be located in the 50 United States, D.C., or Canada to qualify. Offer may be modified or cancelled anytime."
So you aren't going to see it posted anywhere in the stores. It's a Rakuten deal so it would only be posted on the Rakuten site itself, not the store you're buying from. It's applied to your account once you signed up and activated once you make the purchase.