For most of the Artix Mobile Games, progress is saved locally, so if you uninstall/reinstall the app or purchase a new device, then your progress unfortunately will be lost.
However, for BattleGems and BioBeasts, there are ways to save your progress.
For BattleGems, you can connect the app to your Facebook account.
For BioBeasts, you can choose Cloud Save, please read this blog post for more information.