Reading and sticking to the instructions would be a good place to start if you wanted your car seat to stay in place. Making sure that the straps are done up tightly enough will prevent the fabric from moving from a position as easily.
Unfortunately, some seat covers are better than others at staying in place during the journey. Sometimes it’s a good idea to conduct some trial and error to find what works for your car.
Overactive dogs can cause seat covers to shift mid-journey, so teaching your pup to remain in one place might be a good place to start.