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 log in to the PK4 TimeTracker application, you see all the Projects/Jobs in your org and you can start tracking time for Jobs/Projects.

It is not necessary to take any backup as the data is automatically synced to the new device that you logged in to.