I'm not sure if that is normal, try out with a BMW M3 E92 or most RWD for the first time made me spin out at turns numerous times unlike any AWD cars I played so far. My mods were Overhaul+900 Degree Shifter+Input. I was wondering maybe there would be a setup for it just to give it more grip especially to the rear tires. So far, I've search "more grip" and "spin out" around this thread and I have no idea where to begin with so many topics showing up.
btw I would like to say many thanks to matt2380, djotefsoup, JDougNY and all the other Overhaul Modders. NFS Shift really felt alive since I started using this mod