Mostly login details are saved if you have either saved the passwords or you have cookies saving these details. Deleting the cookies folder and not saving passwords would solve the problem and it's not possible that the details are available on all computers like the cafe where you haven't been logged in earlier. Saving login details on your own computer/phone also is dangerous as if your computer/phone gets hacked, the hacker can directly access your account. In the phone as well I keep deleting data everyday and prefer logging in everytime I access the app.
Well it will save your account information if you agree to save it but if you not then you'll need to retype it again if you are logging in which is recommended for our accounts safety, i think cookies has less work about the credentials and it is more about our browsing activities. I think it is just simple, if possible do not use public computers in accessing your wallets or exchange site you stored your money but if not then make sure to watch yourself from clicking too much so that your account will not be in danger. If you have your own device, laptop or phone you can save your account details for it is only you who will use that device.