Contacts are not directly linked to publications. A contact can (in theory) sign in to any web application where the contact information is in the subscription management database (usually called tridion_submgmt) - regardless of which site they signed up on.
When you create a contact, usually you assign it to a global address book (you can have one of these, or multiple). Address books can be shared across multiple publications - so probably all you need to do is ensure that the address book is available in your 060 publications.
Each publication can be configured to synchronize with a (potentially different) front-end subscription management database. Because of this, if you have multiple subscription management databases, it is possible that the address book your contact is created in, is not sync'd to all front-end databases, which would result in the situation where your contact could not log in on all sites.