Will there be a text message reminding the insurance company to pay the owner?

If the SMS is sent automatically by PICC, you should be the owner and PICC is your insurance company.

PICC sends you a text message saying that the case has been closed, indicating that the money has been found on your card, and the insurance company will basically not directly transfer the money to the other party's account unless the court decides to require it.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.