Howdy Meganjp,
Thanks for using the Apple Support Communities.
I see from your post that you've set up Family Sharing, and your sister keeps getting the error "check the payment method," as well as you're wondering about how payments are being billed. To start with, all payments in Family Sharing are billed to the organizer's payment type on file. The only time the organizer's payment type is not billed, is if the family member has credit on their iTunes Store account. The following article explains more about how Family Sharing purchases are billed:
Family purchases and payments - Apple Support
As for the error your sister is getting where it says something to the like of "check the payment method," I'd like you to please first start with verifying the payment method from your iPhone. To do this, go to Settings > iTunes & App Store, tap your Apple ID, then tap View Apple ID. After entering your password select Payment Method, re-enter your security code and expiration date of the card on file, and then tap Done to save the changes. If your sister continues to receive the error after you've re-entered this information, please let us know.
Take care.