Unfortunatley, the Dropbox Passwords app does not support an official iPad app yet. It's disappointing, I agree - especially because a Password manager app is one you want across devices and iPads are more frequently used in landscape mode, especially with a keyboard.
No iPad support? If so it contradicts the app's official description and would explain why I've wasted hours in vain trying to get it working. Furthermore, the reply I had from Dropbox Support after reporting that the app works on my desktpp PC but not my iPad, gave no mention of this.