The subscription purchased on Apple Store is exclusively linked to your Apple ID. It means that the app must recognize this subscription, by logging in the device with this account.
Touchpix includes a log in system, which can be used to log in with the Touchpix account, hence your website subscription will be recognised. However, only the web subscription will be recognised. To use an Apple Store subscription on a different device, you need to log in with your Apple ID in the device settings. Grab the device to which you wish to transfer the subscription, then:
Go to the device settings.
Tap on your name (Apple ID) or log in with the Apple ID containing this subscription.
Tap on 'Subscriptions'.
Check that 'Touchpix' subscription shows and it's not expired.
Go to Touchpix app and scan an event QR code
If an error pops up, tap on 'manage subscription in-app'
Tap on 'restore purchase'
After a short scan, the app will detect your Touchpix subscription and you will be ready to activate the event.