Congrats on the new family member!

Cats can easily take 3 weeks to adjust to a new living situation, with other felines. Since you have only been there 4 days (generous, not sure what time you got home Sunday) I'd say it early days yet, don't worry.

Keep the cats separated. Do a traditional cat introduction. This means first Tyri is in a room, a safe place, with food, water, litter. Make sure family members visit with him. Then have the other cats in a room (food, water, litter), and let Tyri have access to the house for a few hours. He needs to learn the surroundings, the places he can climb / jump, it is all new to him. Sights, sounds, smells. Sure he's been with you humans but he is suddenly presented with other felines! OH NO they could be predators or territorial! Quick, hiss, growl, fluff up your coat to make you look HUGE.

Have all the cats sleeping on small blankets, throws, towels. After 2 or 3 days, swap the towels, so now Tyri has 3 towels, each with the smell of the other cats. Let them sniff one another beneath the door.

After a few days / a week, depends how everyone is going, open the door and let him come out on his own when he is ready. Watch, perhaps even keep a water squirt bottle handy. If a fight should develop, you want to be ready to break it up.

All you can do is set the stage -- the cats will have to sort things out themselves.