for the title at the same time? I was rear-ended and the other party's car insurance company has the nerve to ask for my car and my title. After that, they will send me a check. Is this normal??

I have no guarantee that I'll get a check. The company is called Assurance America. DO NOT INSURE WITH ASSURANCE AMERICA.
They're very SLICK. They send me power of attorney paper work, and the settlement quote. The letter also asks me to MAIL to title back to them. Then Carport the salvage company calls me to pick up the car, the same day. WTF?
I HAVE NOT BEEN PAID YET. NO CHECK YET.

Well, yes, they can't salvage the car until you turn the title over to them. If you're keeping the car, they'll have the title changed to a salvage title, which should then be mailed to you.

Ask them to make the payment to you, and hold back $500 for the title. Then after you get MOST of the payment, you'll mail the title to them (delivery confirmation), and after they get the title, they can mail you the check for the last $500.

Yes. My son totaled my truck 6 months ago. I was lucky enough to be able to settle with my insurance company locally, but they towed my vehicle to their yard and I met them to hand over the title, sign the power of attorney and they handed me a check.

when an insurance company totals out your car and they give you a check , the car is theirs and yes, you have to give them the title. its just like you sold them the car. also they need to check the title to see if you have a loan out on the car as then they will hand the check to the finance company instead of you.