How best to settle adult cats into their new home

[fougere]

Well, we have now arrived home with Mother's cats. They are both rather bewildered (understandably), but Alex did come out of his carrier purring when I gave him a fuss. Then the pair of them cuddled up under the bed, out of sight.
I have left them for the evening to explore their new surroundings and get their bearings. They have a litter tray, their usual dry food, and water in the room.
Am I doing the right thing?
I'm not used to cats, so any suggestions will be gratefully received as I want their stay to be as nice and comfortable as possible while I look for a loving, permanent home for them.

[Crewella]

Bless you, you've done exactly the right thing. It might take a few days for them to gain confidence and come out when you're in the room, but that's fine and happens a lot with cats in new environments so don't worry.

[fougere]

Thank-you for the reply. That's a relief.
I have just checked in on them. They have eaten a bit, but are still under the bed. Chloe is stretched out, looking quite comfortable and relaxed. Alex is usually the bolder of the two, but to me he seems less relaxed about his new surroundings.
That's it for today. I shall leave them until morning, now I know they're still alive!

[Crewella]

It does sometimes work out that way - the more timid ones gain more comfort from the act of hiding away, I guess! If they've already had a bite to eat then they're doing well.