Upon additional discussion here, ProcessPurchase will be called if you are using the new iOS Promotion feature that was added in IAP 1.13. So if you start a purchase on the App Store page, it will open your app and the normal IAP process will happen and ProcessPurchase will indeed be called. The instructions for supporting this feature are in the changelog:
Regarding the payload, that is only used for Google Play and not the Apple App Store.