Purchases on the App Store are specific to the AppleID on which you make them, and are then available on all devices with that Apple ID or within the same "Family" sharing plan.
iSitter doesn't check the store every time it starts up in case something has changed, this would require typing in your Apple ID password each time and would be frustrating for the users.
You can get it to check again, in 3 ways:
• Trying to make the purchase on the new device would tell you you already bought it, and offer it for free
• Apps should have a "restore previous purchase" button, to log into the store and download any purchases. iSitter has one.
• Re-installing the app from the store will bring down its purchased state
For situations where your devices are not on the same AppleID, or within the same Family, once iSitter connects it temporarily transfers all purchases onto both devices until the next time it is closed.