Once I bring the cat down, he should be taken inside the house or other enclosure and released there. First, he will need a few minutes to get reoriented and figure out where he is and determine if he is safe. He will likely be dehydrated and very hungry, so I recommend that you feed him only canned food and add water to it so that it makes a thick soup. He will be tempted to eat more than he can handle, so it is best to regulate his feedings so he does not overdo it and throw it all up. I recommend routinely feeding wet food with added water anyway, but you should give them these wet feedings at least a couple of days to help them get fully re-hydrated. Of course, clean, fresh water should also be available to them at all times. It is highly unlikely that they will drink too much, so let them drink as much as they want.
You should watch the cat to make sure he eventually pees and poops and does so without straining or pain. Male cats in particular are susceptible to blockages in the urethra when crystals collect in the bladder after being dehydrated for a long time. This is a serious condition and will require vet care. Impaction of the bowels is another serious risk of prolonged dehydration, so be watchful for signs there as well.
You can check your cat to see if he is dehydrated simply by pulling up the skin on his back, letting it go and watching how long it takes to fall back into position. The longer it takes, the more dehydrated the cat is. If it falls back into position in less than a second, he is fine. If it takes up to two seconds, he is border-line. If it takes longer, he is definitely dehydrated.
I am not a vet, so please do not take the information I give as qualified veterinary advice. I always recommend taking your cat to the vet to be checked after a rescue, but I also acknowledge that few people do so, and the cat does appear to do well afterward. Still, there may be hidden conditions that a vet can address if the cat is seen in time. Of course, I would insist that you consult with your vet if there is a sign of injury, unusual behavior, lethargy, if the cat is hiding or refuses to eat, or the cat is straining to pee or poop.
Sometimes the cat being rescued is an unknown one, that is, the caller may not know to whom the cat belongs or even if it belongs to anyone. If that is the case, once I rescue him, I can use my microchip scanner to see if he has a microchip. If he has a chip, then we can probably locate his owner. If not, hopefully someone in the area will be able to keep the cat until the owner is found.