C1044 is a code indicating a problem with the right rear 'tone wheel' or the ring that the wheel sensor reads. Additionally, the lights coming on after the vehicle is in motion also indicates a problem at the wheel and not upstream in the system. So, (and here comes the guesses on my part) either the tone wheel is damaged (unlikely on a new part) or you've got the wrong hub assembly/defective part. Does it look like this?
I've not worked on something this new but it appears the pickup/tone ring is inside the hub and covered by the plastic bit. I'm guessing your wheel speed sensor plugs into the hole in the plastic cover. So there's nothing to see there, unlike the older designs.
If the part isn't compatible, such as it has a different number of 'teeth' on the tone ring or the ring isn't the correct diameter that particular wheel will get a speed reading that is different from the other 3 and the system won't recognize it.
2008 has some multiple choices: 2wd and 4wd are different, and depending on when it was made it may have a choice between disc and drum rear brakes. Though I wouldn't expect these parts to be interchangeable, you may want to confirm that the part you bought is correct for your vehicle.