I never used CoinTracking but It should only ask you for an API key which you can create from your Security page in Binance. Make sure to check the 'Read info' permission only so they can only read data and you should be fine. They are probably asking you for login details because you weren't connected when they redirected you to Binance.
Do you use a better one? Try the Tabtrader. You should be okay with it. It can be easily downloaded from the Google playstore on Android. Input the API key (follow the instruction from the poster above) and you are good.
