How does Instagram find my Facebook account?
Apps that use the newer Android standard of data backup will store their basic information on Google's servers... 

Look in Settings - Backup &amp; Reset and there is an option called Automatic Restore (or something similar), it's description literally says "When reinstalling an app, restore backed up settings and data". 

If you do not want the applications data restored, remove the app, turn this option off and reinstall the applications.