Age 13 is important because it's the age of consent in Japan. Perhaps they are in one of the prefectures where there aren't stricter stipulations on the matter...
@Aleph0
But even if they in a prefecture where 13 is the age of consent, adult still cannot lay hands on a minor legally, even if they have 1 year age difference. Given that she's a teacher, her punishment may be even harsher than a typical convict's.
@Faust9 Likely referring back to around CH31-34 when sensei was thinking back to how her email was created by Yae and that email was how she got her wedding invite and pics of her child (Hime).