Car seat help!

So I’m a FTM. My husband and I installed our rear facing safety first car seat the other day. The base that comes with the latch hooks and hooks into the back seat (which is the front of the car seat) is secure and doesn’t move at all; however, the back of the car seat (that goes against our seats) moves and can even be lifted up. Is that normal? I had 3 moms come and look and 2 said it’s not normal while one said it is. Looks like I’ll be taking it to the fire station for them check. 🤦🏻‍♀️