The cats still need a private, easy route in
A puppy who trots to the litter area is usually chasing interesting smells and forbidden snacks, not trying to upset the cats, but a cat interrupted mid-toilet by a bouncy puppy learns quickly that the tray is no longer safe. Protect the route rather than just the box: fit a gate the cats can slip through or jump but the puppy cannot, use a door latch that holds the door open a cat-width, or move one tray into a room that stays puppy-free. Check the solution from the cat's side at night and when the house is busy, because a route that works while you hold the puppy may vanish the moment everyone sits down to eat.
Tray choices that help a cat leave quickly
While the puppy is learning house rules, favor open trays over covered boxes with a single flap entrance that a cat must push through with a puppy waiting on the other side. Place at least one tray well away from the puppy's play and sleeping area, and keep the one-box-per-cat-plus-one count so a cat never has to choose between a disturbed tray and waiting. Scoop more promptly than usual during the puppy's first weeks, since a freshly used tray is the strongest magnet, and store used litter in a lidded bin the puppy cannot nose open. Avoid scattering litter or placing food near the trays to lure cats in, because both blur the boundary you are trying to teach the puppy.
Teach the puppy that the litter zone is dull
Management alone rarely holds once a puppy grows bolder, so pair the barriers with training in short, cheerful sessions. Reward the puppy for looking away from the litter gate, for coming when called from that hallway, and for settling on a mat with a chew in the room where the puppy does belong. If the puppy slips through, interrupt calmly, lead him out, and reward the exit rather than making the litter area the stage for an exciting chase. Supervise all loose time until the habit fades, and use a lead indoors if the puppy makes repeated dashes, because every successful raid rehearses the behavior you want to end.
Health and housekeeping notes for a mixed household
Puppies who eat litter or feces can pick up stomach upsets and parasites, and clumping litter swallowed in quantity is not a snack any puppy should have access to, so persistent raids are a reason to tighten barriers the same day rather than waiting for training to catch up. Mention repeated litter eating at the puppy's next veterinary visit, and call sooner if you see vomiting, diarrhea, loss of appetite, or straining after a raid. For the cats, watch for the opposite problem: a cat who starts avoiding trays, holding on, or urinating near the gate may be telling you the barrier works against the puppy but also slows the cat, so widen the cat opening or add a second protected tray.
Sharing supervision so the boundary holds
This setup only works if every person in the house closes the same gate, keeps the same door latched, and knows who is on puppy watch during the risky after-meal hour. Listing those jobs in KinsLe Care Teams lets you assign the extra scoops, the gate checks, and the supervised free time for the litter area so the cats keep a routine the puppy cannot undo.