The guy at the hitch shop is either a poor communicator or poorly informed. The trailer doesn't "learn" anything about the brake controller.
Now, I found the P3 to be finicky in long traffic engagements. I generally ran it at boost level 2 on the highway but in traffic or around town if I didn't turn boost off entirely, it would start to get "grabby" with the brakes after a few applications in quick succession. I don't know if this is different behavior from the magnets or brakes when they heat up, or some odd behavior of the time+accelerometer guesstimations the Prodigy does or what. And, I changed truck and trailer at the same time so I never towed our original trailer with the new truck with the built-in brake controller.
Still, I experienced something very much like you, with the next model of the Prodigy, on a 2-axle trailer with drum brakes. If there's a boost on the P2 you can turn on and off easily, see if that improves things.
Zero Gravitas — 2017 Flying Cloud 26U | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill