That was sweet of your family to take one of them!
Imagine you're three to six years old. Your parents send you to China. Everything looks different, everything smells different, everything tastes different. There are other children there, and you don't understand their games. Everything you knew that was "home," that was comfortable is gone! You don't know why! You wouldn't feel comfortable in just one week either.
Just like you would be best if given your own room, with its own bathroom, and your own toys, and people just come to sit with you and read out loud to you to help you understand that you can trust them, this is what kitty needs. You wouldn't want to be held by your new mom and dad - you wouldn't necessarily understand that that their reaching out to you is to hug you, and they smell strange. Maybe you're some lab experiment. It is completely terrifying!
New kitty needs to be confined to a bedroom or a guest room or a den or something. Getting a VERY regular schedule going for fresh water, checking food dish, scooping litter will really help. Routines help cats adjust to new environments. Each person should spend as much time in the room as possible - ignoring kitty. Just letting him get used to you. Building his trust that you are all safe, that he is safe, and that this is now home. Read out loud, fold laundry, iron, work on a laptop, paint, sew, whatever. Just be in there, letting him get comfortable with all the new people, all the new smells, all the new sounds.
You can help him de-stress with a product called Feliway. It is a synthetic hormone that mimics the "friendly" markets in cats' cheeks. It's available online and at most pet stores. Just don't spray it near any scratching posts, scratching pads, or the litter box.
Give him a place to hide. If it's a bedroom, under the bed is great. Let him be alone. When he gets curious, he'll come out. He'll use the litter box and eat when you're not around. And if you confine him to his own room, you'll be able to tell. He won't be scared of the other cat - he'll be building his own "safe space."
Let him get comfortable with his new people and in his new environment before you worry about introducing him to your other kitty. Turn off the "clock," and just let him adjust in his own time. After a few days, maybe try play with a wand toy. If he isn't into it yet, let it be.
Spend as much time down at his level as you can. Sitting on the floor doing whatever you can in there. Sit sideways to where he is. Don't look directly at him - if you look at him at all, look at his forehead or over the top of his head. Looking directly at his eyes is a sign of aggression. "Looking" at him with your eyes closed, however, is a fabulous trust builder. Yawn, stretch - do things cats do. Let him see you being relaxed, and he'll come to figure out he's not a lab experiment.
Food is a great motivator. Chicken baby food is also a great treat. Someone in the family, whoever is the person most into the kitties, should put on a t-shirt they don't mind giving up and getting it REALLY sweaty. Put it under the food dish. This will help kitty associate that person with "good" things. If it's important to all of you, rotate the t-shirt under there every week.
If someone's sitting in there and curiosity overcomes him - IGNORE YOUR INSTINCT TO PET HIM. Just sit there and do your best to ignore him. The less you want from him, the less you appear to want to interact with him, the more trust he will have. Cats, especially scaredy cats, are contrarians. Whenever we want attention from our kitties (they were all feral rescues) - we ignore them for a day or two. Completely. Then they're all over us for attention! Let him come sniff you if he comes that close. MAYBE move a hand slowly out towards him on the bias - not right at him - see how he reacts. Guage his fear. If he bolts, it was too soon. If he headbumps you, then pet him.
Try the baby food on a spoon. Sit sideways to him, reach out with it and let your hand rest there. See what happens. He may ignore it the first day or two - but the smell of that yummy treat will usually pull him out.
Let that room be his safe space when you get to the point of introducing the kitties. Good idea is to put up a baby gate to let them see/smell each other. Of course cats can just jump right over it. Some won't. Some people go so far as to temporarily put a screen door on the "cat" rooom. This REALLY helps the intros, because they can see and smell each other and just get used to the idea of another cat - but each one is in their own territory.
Once he's comfortable with you and in his space, move the person-smell t-shirt to his bed, and rub your existing kitty all over with a cloth and put it under new kitty's food dish. In the meantime, maybe when moving new kitty into his room, rub him all over with a wash cloth or rag or whatever, and put that "new kitty" scented cloth under existing kitty's food dish. This will help them to associate each others' scents with good things.
One last thought - cats definitely bond with people. But even more than they are about love and respect, they are about territory. He has been taken out of his and is very upset and confused. He needs to make some space HIS territory. A bathroom works as well, so long as there's enough room in there for him to be comfortable for a few weeks, because it may take that long (or longer - there's just no way to know). But being allowed to hide is VERY important.
That said.... the most important ingredient in all of this is time.