Edit:
All data is completely gone only hidden on both my iPhone and iPad and but I am supposed do have to enter my iTunes password. WTF!? Thanks for nothing Apple. If memory serves this is the second 'deadly' This is just another update to a an otherwise great product.
Users do not enjoy this update!
Developers EZ get your s__t together!!!

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

Calm down

The app uses Apple receipt to validate purchase. Normally Apple won't require Apple ID during update (It is automatically downloaded with the update and first purchase normally). But this time it should be caused by some external reasons that Apple wants you to login to download the receipt (e.g., OS update, or App Store upgrade, or Apple ID switch).

Don't afraid, iOS is secure enough that no app can ever get your account information. The input dialog is outside the app. If you don't input your Apple ID, the receipt won't be downloaded. And the app will not function properly.

I guess this has something to do with Apple rolling out iOS 9. Not Go Eye's fault.