safety first grow and go

ok, I'm confused.. I have the Safety First grow and go convertible seat in my Chevy equinox. It's rear faced but when I installed it, it moves up and down. I have the level on 3 which is as reclined as it gets, level 2 it moves worse. It's as tight as I can possibly get it.. I'm 200lbs and put my knee in the seat while my military husband pulled the latch. I can't move it side to side much, if any..only able to move it up and down. Is this how it's supposed to be? Is it ok it moves up and down? It has a tether but is only for forward facing.

I'm a FTM and all I heard is that the carseat shouldn't move more than a tiny bit so forgive me for sounding ignorant, I want to make sure my Kid's are safe!