Formula fields are calculated on demand, and thus does not participate in the order of execution. In practice, that means it calculated each time it is queried from the database.
In the context of a DML operation, each formula is recalculated while loading Trigger.old and Trigger.new, before evaluating validation, assignment, escalation, and workflow rules, and while executing process builder, flow, and approval processes.
Formula Field calculation in Order of execution
Email-to-Case first takes the incoming email and performs a database save on the Case object. At this point in time, there is no Email Message record saved to the database. The Email Message gets saved later in the process, meaning that the Case Source field is not populated at this time with the Email Message which initiated the case creation. Therefore, when workflow rules fire (and auto response) during the save of the Case record, it cannot find any related Email Message record and so will evaluate to false and move on to the next criteria.
Email Message fields not evaluated by Case auto-response Rules
My guess is even though it doesn't explicitly mention about the formula fields even those are effected by the email2case behavior as formula fields are calculated ahead of workflow rules and there is no Email Message record saved to the database at that point of time