Think about it... if you had a huge vertical tail fin on a 20 foot boom off the back of the car....The car would be a weather vane...it would turn in to the wind no matter what the driver wanted.
You are right but that is a good thing within reason. A station wagon is inherently aero stable in that situation (ignoring issues like roll steer), when hit by a gust of cross wind the rear of the wagon has more side pressure than the front does and the car will yaw slightly into the wind. This means that it self corrects and the driver does not need to make any steering input to stay in their lane. In a car that has very square front fenders like the 1970's Ford Comet. They are a night mare to drive in gusty cross wind as the car yaws away from the wind when hit by a side gust which magnifies the course deviation from the intended path. In our chinook wind storms my Wagon is perfectly happy in a cross wind of 50 mph with gusts to 70 while traveling at 75 mph at right angles to the wind. I feel a slight wiggle when the car is hit by a gust but otherwise have no clue the wind is bad.
On several occasions I have been driving to work and noticed cars ahead of me weaving a bit and braking to slow down for no apparent reason only to realize that there is a strong cross wind I had not even noticed until I passed some trees and could see them bent back from the winds.
This is a good example of why your center of aero pressure is not a fixed and static thing, it can change dramatically if the effective wind is not coming head on to the car.
In the case of a car with a lot of rear sail area like a station wagon a wind at 15 degrees off axis moves the center of pressure toward the rear of the car (an inherently stable situation). A car with a bluff front and square sides (like a roadster) the exact opposite happens the center of pressure moves forward as the wind begins to take an "angle off the bow".
Cross winds can also dramatically change down force. In the 1980's vintage Corvettes a cross wind giving an effective wind vector about 15 degrees off axis would blow the high pressure air that normally collects on the upper part of the hood in front of the wind shield off the down wind side of the windshield effectively dumping all that down force and dramatically increasing front lift. Then as the down force disappeared the front of the car unloaded and lifted increasing the front drag and inducing a yaw away from the wind.
Sometimes the automotive engineers intentionally add roll steer to a cars suspension to help cancel out some of this cross wind motion.
If the car has balanced air drag front to rear when in a quartering wind, it simply moves sideways when hit by a cross wind gust, but maintains its heading (runs over timing lights perhaps), If it has a slight rear ward bias (sail area from a tail fin etc. or a station wagon like body style) it will help the driver stay on course by aerodynamically yawing into the quartering wind. If the side wind drag is biased forward, like a roadster, with square vertical side panels on the engine compartment, and the very high drag or the radiator, the car wants to turn away from the gust. As it does the effective frontal area exposed to the air flow increases (a car has more frontal area viewed at 45 degrees than at 90 degrees and much more than when the wind is approaching head on) aero drag builds much faster on the front of the car than on the rear, as the air is trying to flow over the car body on a diagonal, so it wants to turn around.
If you look at a roadster at an angle of 15 - 20 degrees as the wind sees it at the beginning of a spin, you can see that the front of the car is much dirtier aerodynamically than the smooth trunk region. That means that as the car yaws away from the wind the center of pressure jumps forward a substantial amount, and your CG is suddenly behind the center of pressure, when while running in dead calm it might be slightly behind it.
This is a bad thing