Hey there!
Generally speaking, partners like yourself use the client's credit card on file to purchase and modify apps so that the client bears the monthly cost and not you. This also helps simplify the final handover, as I've seen cases where partners credit cards are not replaced at the time of handover, leading to trouble down the road for the partner, the client, as well as my pals over in billing.
Generally speaking though, apps charge to whichever card is on file. Whenever billing information is changed in the account, the apps charge to the new credit card on file, and shouldn't persist on an older card.
Let me know what you think!
Matthew Buttler
Guru
Shopify Inc.