All cats are territorial by instinct. They take ownership and guard your home against any other invading cats. It doesn't matter if the doors are closed and locked, they don't know that. Guarding an entire house is a huge responsibility and causes great stress. The best thing you can do to help your new cat get adjusted to your home is limit her territory to an amount she can guard without feeling stressed.
So start you new cat out in a small room like the bathroom or bedroom. Keep liter box and food across the room from each other. Watch for her to use her liter box consistently, become relaxed, and at home. Now give her a little more territory, but not an overwhelming amount.
Cats mark their territory constantly. Your cat will patrol her territory and hopefully mark it with the scent of her face. You won't notice this because us humans can't smell feline facial pheromones.

When your cat is stressed and insecure she may mark her territory with urine or feces. That you will notice, or wish you had noticed, right away. It is a danger signal that should never be ignored. Cats will go outside the liter box when they feel sick. A urinary problem can be fatal so always first assume your cat is sick, then consider stress second.
You can increase the feeling of security by adding a cat tree or other places where your cat can get up high off the floor. Most cats can get onto the refrigerator, but that is a resting place of last resort, not an enjoyable place to sleep while feeling safe.
Scratching posts are another must have. Cats scratch to mark territory. Give them something tall, study and covered in rough sisel rope or fabric located promently in your home to help them guard their territory. If you don't they will scratch something else.
Just having these things isn't enough. They must be located well. Liter boxes can not be out of sight and out of mind. Your cat thinks of the liter box as a valuable resource and territory so treat it that way. If your cat isn't using her scratching post or cat tree move them to where your cat spends her time.

A cat tree in the corner away from everything and everyone doesn't work. Move that cat tree in front of the big window where people gather to talk and watch television. Move that scratching post near the door so that any stray cats will smell it first thing when (if) they walked into your home.