The school paid the medical insurance and received the SMS reminder.

That means the school didn't hand it in.

If you don't pay the medical insurance when it is due, there will be some text messages. If it is prompted by SMS, you need to pay professional medical insurance fees on your mobile phone or at the place where you pay medical insurance. So in general, if there is no continuous payment, you don't need to pay in time when you receive the text message.