Yes, both need to be first time buyers.
If the First Home is being purchased by a couple (who are married, in a civil partnership or living together) but only one of them can obtain a mortgage (e.g. where one of the couple has a poor credit history) it is still possible to progress with the First Homes scheme, but both adults in the couple must be first time buyers and both will need to complete the Application Pack, supply the supporting evidence documents and sign the Legal Declarations that they meet the First Homes Eligibility Criteria.