I personally don't combine foster cats with my resident cat because he is very cat-aggressive, but I will introduce my (very calm, cat-loving, with an instant "leave it" or "come here" response) dog to them for short periods. We start with a baby gate between them and that usually goes well, though we've had one cat try to charge him through the gate!
My organization enforces a minimum 2 week quarantine period before introducing fosters to the family pets, just in case. An incident a couple years ago that resulted in 12 cats (half of them semi-feral barn cats) with ringworm taught us that lesson the hard way :(
However, I also just talked with a foster last week whose kittens we discovered had (a couple) fleas at their spay/neuter appointment. She's had the kittens since they were a few days old, never seen any signs of fleas, and I've been over several times and never seen anything either. Since she keeps her foster kittens 100% separate in their own room, clean up/treatment has been relatively easy.
#FosteringaPet