InApp billing just charges the user and tells your app whether it was successful or not. It is up to you to figure out how to give the user what they purchased.
You can...
toggle the SharedPreferences of the app to save their purchase. Obviously multiple people can use the same app on the same device with the purchase.
provide login functionality to save a purchase to a server, in case the user deletes the app or gets a new device.
Use one-time purchases to check whether the user has purchased previously. This won't carry over to several accounts on different devices/multiple-accounts-per-device.