Nothing to worry about your data, all the Clock-In/Out and the Check-In/Out details are saved in Salesforce servers.

When you download the app on a different device and login to the PK4 TimeTracker application using your login credentials, you see all the Projects/Jobs that are in your org and you can start tracking time for the Projects/Jobs.

You need not take any backup of the data as the data is automatically synced to the new device that you logged in.