When a contact is created via the API, are there conditions under which it will not be associated with an Integration and/or filterable with a given integration (see below screenshot)? I assume this is by API key since I don't see any other way to define an integration/source in https://developers.hubspot.com/docs/methods/contacts/create_contact.
That screenshot looks like the 'Filter activity' dropdown on a particular contact's timeline. The 'Integrations' section of that dropdown allows you you filter by custom integration events; the integrations listed in that dropdown will appear for all contacts. If you select those integration filters, custom integration events may appear in the contact's timeline. They don't have anything to do with the source of a contact, but may show if a contact is 'associated' with an integrations (i.e. if the contact has and events for a given integration).
Does that help answer your question?