I personally never use the “Ask to add/updated existing login” features, so I can’t say for sure (unless I set up a test later).
It makes sense (to me) that the “Ask to add login” function for saving new logins would present a simple yes/no interface instead of opening the full “New login” screen in the browser extension. Thus, I am not surprised that it would save the login in the default location (which is the user’s individual vault); as I mentioned previously, there is a feature request proposing the ability to customize the default ownership/collection for new items.
If that is the case, you would indeed need to move the added new login into an existing collection, if you want the item to be shared. You can do this in bulk, using the Web Vault.
However, if you have enabled “Ask to updated existing login”, then I assume that confirming a password update using the interactive prompt will directly update the credentials in the shared collection, no additional steps required.