The DigiSaw Puzzles app stores puzzle information and images on your mobile device so that create and solve jigsaws on your device.
The information captured by the app stays on your device unless you have chosen to store your puzzles in iCloud in which case the information will be autoatically uploaded to your private iCloud storage area.
If you have chosen to store your puzzles in iCloud and you have more than one Apple device associated with your Apple account your data will be automatically shared between your devices. This is done for convenience to ensure that you enjoy solving your puzzles on any of your devices.
Your data is never shared with Today's New Idea.