This is common for me too. I'm in the process of training my own model from my own images I collected from my cameras hoping that this can help with more accurate detections. For your situation I might try to increase the min object size under the motion sensor settings. Making that larger can help stop it from detecting the motion from the cats and therefore stop sending cat images to deepstack as often.
Here is my problem with using Min Size Target Filters. It starts with the fact I want to get a trigger and alert as early as possible when a person enters the Intrusion Zone or crosses a Tripwire. For my use case, I have a 4mp varifocal zoomed to its maximum setting of 12mm. This provides me a viewing range from about 5 ft in front of the camera out to about 150 ft away from the camera. Ideally, I want a trigger/alert at 120 ft from the camera, so that is where the IVS Intrusion Zone extends as well as Tripwires set. Cats come into view and cause false positives at between 5 ft to 20 ft from the camera. If I set a Min Size to prevent cat alerts at 10 ft from the camera, it's a Min Size of more than 1,000 pixels. OTOH, a 6 ft tall person at 100 ft away is no more than 700 pixels. The Min Size to prevent detection of cats also prevents early detection of potential intruders. While true that as the person comes closer they will (or should) be detected, I've lost the 'edge' of earlier detection.
At this point due to IVS rules being unreliable, I now use IVS along with SMD for Triggers,
and Deepstack for Alerts. It works, so I am hopeful AI will continue to improve in eliminating false positives, and also eliminating many of these 'work-arounds' necessary for the current state of AI.