So first a little bit of information:
Auto Complete is not filling in the login form, a password manager is. Modern browsers will NEVER have auto complete remember a login form!
Password managers are NOT a security flaw or point of attack. An unprotected/poorly designed system, bad users, and bad policies are.
Most browsers these days implement a password manager into their browser(NOT auto complete) that keeps things in a safe and secure location(for google chrome, it's actually stored in your google account cloud). In google chrome, firefox, and edge you can disable the password manager and it will not affect auto complete. This is because auto complete and password manager are two separate sub programs running in the browser. autocomplete=off on a form does not say "Don't Fill In A Form", it says "Don't Remember This Form". However a browser will still probably fill in a login area and ask to remember it because password managers are not auto complete, and thusly ignore this. If the password manager is turned off and you go to a login page, it will not automatically fill in the form even if auto complete is turned on. This is because of the way most modern browsers implement auto complete and their built in password managers. What does this mean? Well it means you, as a web developer, have NO CONTROL over a users browser program itself, just the web page. As such you cannot prevent the password manager form remembering the password, just the same as you can't prevent the user from writing the password on a sticky note or in the mud.
So what can you do to prevent this? Nothing. That's not a bad thing though. You just need to build your website, applications, and services as secure as possible so that if something gets compromised, as little damage as possible happens to your service.
If a security expert tells you a password manager is a security flaw, ask them how they manage their randomly generated, routinely updated secure login credentials and private keys. Then find a new security expert!!!
That being said, a password manager is not something to be feared. It can actually be a GOD send for storing randomly generated, routinely updated enterprise level passwords.
There was once an
autocomplete=off attribute on forms, but this attribute is deliberately ignored in most browsers (Chrome, Firefox, IE) for a while, see The autocomplete attribute and login fields. So the answer is probably that the website has no control if these information are saved or not.