I have two Yorkies and four cats. When I got Brody, no problem with him and the cats...but he wasn't raised with cats. He just pretty much ignored them, and they were cautious of him due to a Chi who became possessive of me and began to 'disallow' the cats from sharing my lap with her.
Brody didn't care who was on or near the lap, or where anyone was.
Several months later, we had rolled up an area rug to take out on the deck and pressure wash and a cat jumped on the backing of the roll and began to 'sharpen' his claws and I yelled at him to quit. Brody became "King of the Cats" in that instant, and now feels he can "correct" their behavior, and "explain" the rules the "Brody Way" at times, but mostly, we have peace at home. I watch his body language any time there is a cat around and intervene before anything starts...most of the time successfully, but he will, at times chase them...he doesn't do anything when (if) he catches up to them and neither has been hurt at all. The cats are at least as big as he and Mia are, most are larger than him and Mia.
Mia, on the other hand, L.O.V.E.S cats, specifically "HER" kitty...but she tries soooo hard to befriend all the cats. She and "HER" kitty love on, and kiss, and preen each other, snuggle up together, etc., but...sometimes Mia is too forceful in her kissie-face-ing and "HER" kitty has not only protested but has 'thunked' her chin to the floor with his paw holding her head on the floor afterward...to keep from drowning in puppy kisses, I think.
The Shih Tzu I puppy sit for also chases "her" kitty, and they have worked out the "order" of things. In fact, the kitty accidentally got locked out of the house and in the screen room one day because he's gotten 'bolder' now hat he's got a new friend and decided to accompany his Shih friend through the door for her morning walk. Poor kitty was a mess by the time Mommy came home from work because there was a huge thunderstorm and pelting rain that day.
I don't know what to advise you to do...they will likely work it out as others have said. Good Luck!