They only get to see the shared vault, right? My personal vault is only accessible to me? Is that how it works?
1Password Version: Not ProvidedExtension Version: Not ProvidedOS Version: Not ProvidedSync Type: Not Provided
If you're using the built-in account system and inviting them such that they set up their own Master Password and receive their own Secret Key then yes, that is correct. If you share your Master Password and Secret Key with someone else then they are you, as far as 1Password is concerned, and will have access to everything you do.
Instructions on how to set this up properly (i.e. not sharing your credentials) can be found here:
Oh, I would never share my credentials, Ben. I just want my personal vault to not be accessible by the kids.
Yep; as long as you use the instructions above then it'll be as you desire.