They click renew, it shows the basket, they click to pay, then they pay. It's basically how you already described. I believe it's possible to bypass the basket if no terms and conditions are enabled, only 1 payment method is available, no coupons are available to redeem, and invoice address is turned off. There's pretty strict requirements to bypass the basket (basically it has to have little to no purpose in order to skip it).
Our current usage is very standard though. A site like amazon you'd add something to your shopping cart, go to your shopping cart, then pay. Same for basically any site with basket functionality. So I really have a hard time understanding the confusion unless they've never purchased anything online before.