Day 1 in a new home is scary for cats – maybe a few days after that too.  Your new cat doesn’t know what just happened to them.  Although it’s tempting to immediately try to include them with the rest of the family, we recommend starting them in a small, enclosed space to start such as a bathroom or small bedroom.  Make sure they can easily find their litterbox, food, water, and they can hide if they get scared.  This lets them start to get used to the sounds and smells in your house.  A small space may feel confining to you, but to them it feels safe because it gives them fewer places they have to check for danger.  You should visit them often to reassure them they aren’t alone and let them start to get used to you.  Failure to do this could result in aggressive behavior toward other animals and people, or urination outside of the litterbox to create a defensive barrier.  

If you have other pets, it’s very important to give your new cat time to adjust to his new environment before introducing him to other animals in your home.  Get small cloths, enough for each pet, and wipe one on each animal’s mouth.  Put the cloths near the other animals’ food dish so when they meet for the first time, they associate the other animal with something positive (food).  Let animals smell and play with each other under the door as a safe early introduction activity.  Make sure to be calm and relaxed when introducing animals as they can smell the chemicals you release when you are nervous or stressed.  After a few weeks, let animals meet each other for short periods of time slowly lengthening the time they are together.  Do not leave them unattended together until you are sure they are getting along.  Some animal pairs can never be left alone together.  

This is a great article with additional information on introducing your pets.

 https://be.chewy.com/can-socialize-cat-tips-introducing-cats/ 

Act2Rescue.com