He says “con ogni probabilità”, and makes no blanket statement: he does not appear to be making the statement that every literary work or inscription of private character used the Ionic script during the period before 403 BC, just that some did.
Even if we knew that the Ionic script was used for the play as first written, note Threatte’s discussion of ε and η, which claims that 460-430 (this play was 425), was the period of greatest confusion between ε and η in the Ionic script in Attica due to the multiple alphabets in use.
