With the girls, I set up their kitty trees ASAP before letting them run free so that there would at least some some familiar scents in the house and I made sure to keep their litter box close to them.
Other than that, I let them explore the house when they wanted. I would try keeping things relatively quiet for the next few days and don't have too many visitors over--I found that people coming over stressed Galina out even more and she didn't want to come out.
If they're not introducing a new member of the family, I would keep all the doors open for him and just let him explore when he's ready to.
He'll come around in time. Cats just like to do things on their terms.
And they're right in not letting him outside just yet. If they want to keep him as an indoor/outdoor cat, I would suggest not letting him out for at least a few more months and when they do start letting him out, have it be on leash at first so that he can be supervised and will not run off if something scares him. This will help him safely get used to his new territory.
Most cats don't like to have their food and water near the litter box, and it can become unhygenic, so I would suggest them move one of the items to another room that is not far away, but does cause the cat to come out some--even if it's only at night when everyone is sleeping.