If your cat is spayed, it's probably more a territory issue.
Cats are never satisfied with their own patch, they do like to poke their noses into other cats' personal spaces. This resolves in two ways - either the sitting tennent defends his or her area successfully, and the interloper tries elsewhere, or the incoming cat takes over, and gives the resident a hard time.
The results depend entirely on the individual characters involved - some cats can't be bothered to make a nuicance of themselves, some cats don't care who poops in their garden.
As advised, it will shake out to their mutual agreement in time, so let them get on with it. If your puss is being bullied, then that's the time to intervene, but otherwise, it's just cats doing what they do.