If I have multiple devices (all iPhones) using a single Apple ID, how do I know which device made a specific app purchase?
Is there a way to tell which apps were bought on each iPhone by looking at the Apple ID "purchased" list of apps?
No, there is no way to identify which device bought any app. You can also buy apps using iTunes on any computer logged in to the same Apple ID. If you want to control apps on phones you need to have a separate iCloud account for each device, linked using Family Sharing. Family Sharing - Apple Support