Hello, by new strong password you probably mean Generate Strong password option in our browser extension popup (the one is show when you click on key icon in browser toolbar). This password is not being stored anywhere as it is just standalone password generator function. It gives you strong password whenever you need it., you can then copy it to clipboard and paste it to registration form for instance.
In some cases we provide password generator to the website, then it is shown in the website form as key icon with asterisk and in case you will use it there, we remember the last one you have generated and from that moment we are watching whether you have that stored and we offer this password on next login to the website if we don't find it stored in your passwords storage. In such case we show a dropdown under the login form with options to use it, discard it and let decision to later time.
The password generator function is extremely useful when you decide to change the password for the website, but note, that you still have to do it on the website itself, changing password just on side of password storage has no effect on you login credentials website provider consider as valid. In most of the cases we should be able catch such change and prompt you to update the login details you have stored with us. And in case you have used generator for password change form on the website itself we also provide the above mentioned fallback solution for the case we don't detect the password change operation on the web.
Let me know if you have any further question related to this topic. In case you have questions on different topic, please create separate thread for it.