Try getting you dog all tired one afternoon, then go out to the backyard or a local park, pitch the tarp and just see if the dog will settle down and take a nap. take a short rest and then go home. repeat again at a different location.
Then try it at night. Set up the tarp, get inside, hang out until the pup settles down or goes to sleep, reward, pack up, go home. shouldn't take more than a half hour. just make sure you have a tired dog when you start.
Then your dog is learning that the tarp is a safe place to rest and let his guard down in a safe known environment.
Plus if he doesn't settle down, you are not all tired and crabby. just go home and work on it a few days later.
Also regarding campsite selection once you go out hiking. Be aware of game trails. I don't care how good a dog is, they are gonna be on alert if there is a deer walking by every 45 min.
At the end of your day if you come to a spot and your dog lays down and sacks out. That is probably a good spot to camp.
But if you are cooking dinner and your pup seems on alert and is roaming around smelling the air, you may want to move on a little and find a place that your dog seems more relaxed.
You may have to ditch the awesome spot above the cliff that is funneling smells from the huge watershed below. You dog may be more relaxed tucked away in some bushes well off the trail. I don't where your dog will sleep best but you will learn with time.
I clip a tiny led light to my dog Benny's collar. It makes him easy to find at night. And gives me a little peace of mind.
Remember dogs and humans have been sleeping outside LONG before silnylon, and long before tents or tarps.
Whats your dogs name?