You don't need a mobile app to make physical transactions using your AAdvantage® Debit Card, but keep in mind that some online transactions may require you to authenticate a transaction attempt via the app. And some functionality is only available via the mobile app.
You should also keep the latest version of the app installed to manage your account; this will help you keep an eye out for suspicious activity and freeze the card in the app should you need to.
AAdvantage® Debit Card doesn't require top-ups as it connects directly to your bank account. This means that you also don't need WiFi access or international data roaming that may incur charges.