I got both of my cats as kittens after my dog was full grown. When they were kittens, they were left in a separate room when I couldn't supervise because they were so small, even a friendly play could hurt them. Then, when my first cat grew a bit, she had a room with a baby gate that only she could access. When the second cat came along, we lived in a house that strangely had a cat door from the kitchen to a sun room, so the cats could go in there if they felt bothered. I don't have anything like that now.
For basically their whole lives, my cats have been left home with my dog all day. All of them seem to just keep to themselves and sleep. Once my dog is used to a cat, he really doesn't acknowledge their existence.
Mikko (USDAA) MAD, SAM, JM, GM, RM, SS; (NADAC) EAC, EJC, TN-E, TG-E, WV-O, OCC, HP-O, VerO; (AKC) NAJ, CGC; NW1 - 8 year old GSD