Your sister's insurance has no bearing, so don't worry.
All that matters is that the driver of the vehicle had insurance when it was being used on a public road. Your insurance was covering you at the time, so you will be fine. If the other party have admitted liability (and in a rear-end shunt, it is always assumed that the driver of the car which ran into the other is at fault), their insurance should settle the claim quite quickly.
Of course, if your sister had been driving at the time, it would be a different story.